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Behavior and mixing of a cold intermediate layer near a sloping boundary

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As in many other subarctic basins, a cold intermediate layer (CIL) is found during ice-free months in the Lower St. Lawrence Estuary (LSLE), Canada. This study examines the behavior of the CIL above the sloping bottom using a high-resolution mooring deployed on the northern side of the estuary. Observations show successive swashes/backwashes of the CIL on the slope at a semi-diurnal frequency. It is shown that these upslope and downslope motions are likely caused by internal tides generated at the nearby channel head sill. Quantification of mixing from 322 turbulence casts reveals that in the bottom 10 m of the water column, the time-average dissipation rate of turbulent kinetic energy is 𝜖 10 m = 1.6×10−7Wkg−1, an order of magnitude greater than found in the interior of the basin, far from boundaries. Near-bottom dissipation during the flood phase of the M2 tide cycle (upslope flow) is about four times greater than during the ebb phase (downslope flow). Bottom shear stress, shear instabilities, and internal wave scattering are considered as potential boundary mixing mechanisms near the seabed. In the interior of the water column, far from the bottom, increasing dissipation rates are observed with both increasing stratification and shear, which suggests some control of the dissipation by the internal wave field. However, poor fits with a parametrization for large-scale wave-wave interactions suggests that the mixing is partly driven by more complex non-linear and/or smaller scale waves.
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Ocean Dynamics
DOI 10.1007/s10236-014-0799-1
Behavior and mixing of a cold intermediate layer near
a sloping boundary
Fr´
ed´
eric Cyr ·Daniel Bourgault ·Peter S. Galbraith
Received: 1 August 2013 / Accepted: 29 November 2014
© Springer-Verlag Berlin Heidelberg 2015
Abstract As in many other subarctic basins, a cold inter-
mediate layer (CIL) is found during ice-free months in
the Lower St. Lawrence Estuary (LSLE), Canada. This
study examines the behavior of the CIL above the slop-
ing bottom using a high-resolution mooring deployed on
the northern side of the estuary. Observations show suc-
cessive swashes/backwashes of the CIL on the slope at a
semi-diurnal frequency. It is shown that these upslope and
downslope motions are likely caused by internal tides gen-
erated at the nearby channel head sill. Quantification of
mixing from 322 turbulence casts reveals that in the bottom
10 m of the water column, the time-average dissipation rate
of turbulent kinetic energy is 10 m =1.6×107W kg1, an
order of magnitude greater than found in the interior of the
basin, far from boundaries. Near-bottom dissipation during
the flood phase of the M2tide cycle (upslope flow) is about
four times greater than during the ebb phase (downslope
flow). Bottom shear stress, shear instabilities, and internal
wave scattering are considered as potential boundary mix-
ing mechanisms near the seabed. In the interior of the water
Responsible Editor: Alejandro Orsi
F. Cyr ()·D. Bourgault
Institut des sciences de la mer de Rimouski,
Universit´e du Qu´ebec `a Rimouski, Rimouski,
Qu´ebec, Canada
e-mail: frederic.cyr@nioz.nl
P. S. Galbraith
Maurice Lamontagne Institute, Department of Fisheries
and Oceans Canada, Mont-Joli, Qu´ebec, Canada
Present Address:
F. Cyr
Royal Netherlands Institute for Sea Research (NIOZ),
’t Horntje, Texel, The Netherlands
column, far from the bottom, increasing dissipation rates
are observed with both increasing stratification and shear,
which suggests some control of the dissipation by the inter-
nal wave field. However, poor fits with a parametrization for
large-scale wave-wave interactions suggests that the mixing
is partly driven by more complex non-linear and/or smaller
scale waves.
Keywords Turbulence ·Boundary mixing ·Cold
intermediate layer ·Lower St. Lawrence Estuary ·Internal
tides ·Internal wave ·Shear instabilities ·Bottom shear
stress
1 Introduction
In a recent study, Cyr et al. (2011) concluded that although
not dominant, boundary mixing can contribute significantly
to the mixing budget of the Gulf of St. Lawrence, a semi-
enclosed subarctic sea located in eastern Canada. That study
was carried out at the Rimouski section, a transect extend-
ing across the Lower St. Lawrence Estuary (LSLE), off
Rimouski (Fig. 1) and was based on the analysis of hundreds
of historical CTD profiles and approximately a thousand
new turbulence profiles collected close to, and away from a
sloping boundary. The study compared observations of ver-
tical mixing rates with those inferred by the summer erosion
of the cold intermediate layer (CIL), assumed to act like a
horizontally uniform passive tracer. However, mixing mech-
anisms were not identified. It was suggested that bottom
shear stress and internal waves may be the principal mixing
agents at sloping boundaries, but the behavior of the CIL
where it intersects the sloping bottom was not investigated.
A first goal of the current study is therefore to exam-
ine the behavior of the CIL near sloping boundaries
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Tadoussac
Rimouski
PointedesMonts
Head of the Laurentian channel
(Internal tides generation site)
N080
70oW 30’ 69oW 30’ 68oW 30’ 67oW
48oN
20’
40’
49oN
20’
Longitude
Latitude
Cabot
Strait
Laurentian
Channel
Gulf of
St. Lawrence
Quebec
USLE
LSLE
Depth (m)
0 100 200 300
yx
Fig. 1 Bathymetry of the Gulf of St. Lawrence (upper inset)
and the Upper (USLE) and Lower St. Lawrence Estuary (LSLE).
The square box in the upper inset correspond to the LSLE where the
study was realized (main figure). Isobaths 20, 120, 200, and 300 m
have been added. The dashed-line is the Rimouski section across the
estuary. Second inset shows details of the study area on the northern
portion of the transect, between isobaths 20 and 120 m (shown with
20-m intervals). Positions of mooring N080 (white star) and of the 322
VMP profiles used in this study (purple dots) are also presented
and the mixing mechanisms responsible for its erosion.
Since numerous past studies have discussed the generation
and propagation of an internal tide generated in the LSLE
(e.g., Forrester 1970,1974; Ingram 1979, Wang et al.
1991; Galbraith 1992), a second objective is to quantify to
what extent the CIL behavior and the mixing are
controlled by internal tides. This last point is also relevant
to other coastal basins since recent studies suggest
that internal tides (or near-inertial waves in the absence
of tides) can partly control the dynamics (stratification,
shear, and dissipation) and mixing of coastal basins
and lakes (e.g., MacKinnon and Gregg 2003; Carter et
al. 2005; van der Lee and Umlauf 2011; Bouffard et al.
2012).
In order to achieve these goals, a field experiment was
carried out in a region where the CIL intersects the slop-
ing bottom on the northern side of the Rimouski section.
Mooring observations are first compared with the solu-
tion of the internal wave equation in order to determine
if the CIL behavior near the boundary may result from
internal tide forcing. Then, semi-diurnal modulation of
turbulence is addressed from vertical microstructure pro-
files. Results suggest that different mixing dynamics are
in play in the water column interior than in the near-
bottom. A comparison between observations and existing
mixing parametrizations is also made to give insights into
the mixing mechanisms at work.
2 Study area
The St. Lawrence Estuary is commonly defined as the
region between Qu´ebec city (just beyond the upper limit
of salt intrusions) and Pointe-des-Monts, where begins the
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Gulf of St. Lawrence (e.g., Forrester 1974; El-Sabh 1979;
Koutitonsky and Bugden 1991) (Fig. 1). The estuary is gen-
erally subdivided into the Upper and Lower St. Lawrence
Estuary (USLE and LSLE, respectively) by a shallow sill
at the head of the Laurentian channel near Tadoussac. The
deep (>290 m) Laurentian channel begins at the continental
slope, runs across the Gulf, and ends near Tadoussac where
the total depth abruptly shallows from 325 m to about 50 m
in less than 15 km.
The LSLE width varies from about 44 km at the mouth
to about 13 km at the head. Because of its unusually large
width for an estuary (about five times the internal Rossby
radius) and because its water masses properties are similar
to the Gulf of St. Lawrence, the LSLE is also commonly
considered to be part of the Gulf. In winter, the major part
of the Gulf of St. Lawrence is characterized by two water
masses: a surface layer near the freezing point and a warmer
and saltier deep layer of oceanic origin. For the rest of the
year, the system is stratified into three water masses after
a surface layer is formed as a result of the spring freshet
and increasing air temperature. The previous winter surface
layer then becomes trapped as a CIL between two warmer
layers (e.g., El-Sabh 1979; Koutitonsky and Bugden 1991;
Galbraith 2006; Smith et al. 2006; Cyr et el. 2011). Once
regenerated during the winter, the CIL properties are slowly
eroded during summer months as a result of mixing (in the
estuary, its core temperature warms at a rate of 0.24 C
per month while its thickness decreases at a rate of 11 m
per month; Gilbert and Pettigrew 1997; Cyr et al. 2011).
Because of winter low surface layer salinities in the LSLE
that inhibit mixing and convection, the CIL is not formed
there but is rather advected from the Gulf during the sum-
mer months as the result of the estuarine circulation (e.g.,
Galbraith 2006; Smith et al. 2006).
The large dimensions of the LSLE also support the gen-
eration of internal tides. These are generated at the sill near
the head of the Laurentian channel and emanate seaward
out of the estuary (e.g., Forrester 1970;1974; Ingram 1979;
Wang et al. 1991; Galbraith 1992). Forrester (1974) was
first to describe the internal tide by fitting density elevation
observations to theoretical vertical modal structures in the
LSLE. He found that at the M2frequency, the internal tide
to be consistent with a Poincar´e-type wave in the second
vertical and first horizontal modes with a wavelength of
about 60 km along-channel. He also found evidence of
Kelvin waves at the diurnal frequency. Wang et al. (1991)
focused on the evolution of the internal tide energy field
along the estuary with three moorings along the LSLE.
They suggested that after its generation at the sill, the semi-
diurnal internal tide propagates with decaying amplitude,
typically with vertical isopycnal displacements from about
80 m at the generation site to about 30 m, 140 km down-
stream, i.e., 40 km downstream of the Rimouski section.
3 Datasets and methodology
3.1 Mooring data
A mooring was deployed between September 20 and Octo-
ber 12, 2011 on the 83 m isobath of the north shore of
the estuary (N080, Fig. 1), in a region where the bottom
slope is approximately constant at 3 % from 40 to 120 m. It
was equipped with one Acoustic Doppler Current Profiler
(RDI Workhorse ADCP, 600 kHz) at 59-m depth, look-
ing downward to the bottom, and 8 RBR Ltd. thermistors
between 30–79 m. Thermistors at 30, 40, and 50 m depth
were equipped with pressure sensors (model TDR-2050),
while the others (60, 65, 70, 75, 79 m) only measured
temperature (model TR-1060). The mooring summary is
provided in Table 1. All thermistors are expected to have a
precision better than 0.01 C. Raw velocity measurements
have an error (defined as the statistical standard deviation
on measurements) of 8.1 cm s1on each 3-s ensemble.
Currents have been rotated by 33.5to produce along-
shore (u) and cross-shore (v) velocities. Velocities in the
bottom 1.5 m above the sea bed have been discarded to
avoid side-lobe contamination of the near bottom velocity
field. Unless otherwise specified, current velocities have
been smoothed using a 5-min averaging window to reduce
the error to 1.4 cm s1.
3.2 Fine- and micro-structure data
Turbulence measurements were collected during summers
2009–2012 with two free-fall, loosely-tethered, vertical
Table 1 Mooring information
N080
Total depth (m) 83
ADCP depth (frequency, orientation) 59 (600 kHz, down)
ADCP range (m) 61-bottom
ADCP sampling freq. (Hz) 1
3
Thermistors depth (m) 30, 40, 50, 60, 65, 70, 75, 80
Thermistor sampling freq. (Hz) 0.2, 0.2, 0.2, 0.1, 0.1, 0.1, 0.1, 0.1
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micro-structure profilers (VMP500) manufactured by Rock-
land Scientific International (RSI). Along with other sen-
sors, these profilers are equipped with two airfoil shear
probes that allow measurements of micro-scale (1 cm)
vertical shear u
z(see Cyr et al. 2011 for other sensors). They
are also equipped with fine-scale (1 dm) temperature-
conductivity-depth (CTD) sensors manufactured by Sea-
Bird Electronics.
A total of 1644 casts have been collected in the region.
Statistics from a portion of this dataset have been published
in two studies (Cyr et al. 2011; Bourgault et al. 2012). For
the purpose of this study, 322 casts collected over the north-
ern boundary of the channel during summers 2010–2012 are
considered (see Fig. 1). For all these casts, the VMP hit the
sloping bottom at depths varying from 20 to 110 m (> 80 %
in the 60–110 m range).
An Acoustic Doppler Current Profiler (RDI Workhorse
ADCP 300 or 600 kHz) was mounted overboard of the small
craft boat used to collect the turbulence profiles, at about
1 m below the surface and looking downward. Although
the vertical bin size and the ensemble length were vari-
able between sorties, the ADCP data were averaged into
4-m bins and 5-min time intervals during post-processing.
The error for these averaged measurements is expected to
equal or less than 1.4 cm s1. This allows the calculation
of the mean shear S2=u
z2+v
z2. Approximate
noise level on the shear determined from spectral analysis is
S2
n1.3×105s2(not shown).
The dissipation rate () of turbulent kinetic energy (TKE)
was calculated from u
zusing standard procedures (see
Cyr et al. 2011):
=15ν
2u
z2,(1)
where ν=f (T ) is the kinematic molecular viscosity as
function of temperature and the overline indicates here a
vertical 1 m bin average. The shear variance u
z2was
obtained by spectral integration to remove random noise.
Turbulent diffusivity was calculated from the dissipation
rate and stratification as:
K=Γ �
N2.(2)
Here, N2=g
ρ
∂ρ
z(with the depth zdefined positive down-
ward), the background buoyancy frequency squared, with
density sorted to remove inversions and averaged in 1-m
bins to match resolution, and Γis an indicator of the
mixing efficiency, which we will refer here as the flux
coefficient, according to Smyth et al. (2001).
A common practice is to calculate the diffusivity using
the constant flux coefficient Γ=0.2 (e.g., Osborn 1980;
Moum et al. 2002,2004; Burchard 2009; Holtermann et al.
2012). On the other hand, Shih et al. (2005) proposed a
parametrization for the mixing efficiency that depends on
the turbulent activity, or the buoyancy Reynolds number
Reb=
νN2, leading to mixing efficiency significantly
lower than Γ=0.2 when the turbulence is fully developed
(Reb>100). This parametrization, tested by Fer and Widell
(2007) and recently used by van der Lee and Umlauf (2011)
for the coastal ocean has the form:
Γ=2Re1
2
bif Reb>100,
0.2 otherwise.(3)
The applicability of this parametrization on microstruc-
ture observations has recently been called into question
by Gregg et al. (2012) who opted for the traditional con-
stant value until some contradictions with oceanic obser-
vations were resolved. Here, we present the result of both
parametrizations, although diffusivity values discussed in
the text have been calculated using Γ=0.2, consistent with
previous studies in this area (Cyr et al. 2011; Bourgault et al.
2012). Averaged values for turbulent variables presented
in this study (N2,S2,and K) were calculated assuming
log-normal distributions (Baker and Gibson 1987).
3.3 Phase averaging
Hourly tide levels were obtained using the xtide software
(www.flaterco.com/xtide) for the city of Rimouski. These
predictions are based on harmonic analyzes of archived
water level records and do not take into account storm
surges or other meteorological effects. Over the 3-week
mooring deployment, the predicted high and low tides were
off by at most 2 min with the observations (not shown).
Some of the temperature and current data presented in
this study are plotted relative to the M2tidal cycle. To do
so, the closest high tide was first identified for each mea-
surement (cast or mooring current profile). Then, the M2
period (12.42 h) was split into 13 classes relative to the time
of the closest high tide (t= [6,5,4, ..., 4,5,6]h)and
the mean value or profile for each class was calculated. Neg-
ative and positive classes correspond, respectively, to ebb
and flood phases of the tidal cycle.
4 Observations
4.1 Cold intermediate layer behavior at the slope
An overview of temperature and velocity fields for the
mooring deployment duration is presented in Fig. 2. Tem-
perature and velocities are low-pass filtered with a 25-h
cut-off period to highlight sub-tidal dynamics. The CIL is
defined here as water temperature below 1 C (Cyr et al.
2011) and is contoured in Fig. 2b with a thick black line.
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Fig. 2 Temperature and
currents measured for the
duration of the mooring
deployment. aPredicted tide
water level at Rimouski (L). b
Evolution of the temperature
field for this period as measured
by the thermistor chain.
Temperature was linearly
interpolated between thermistors
and a 25-h low-pass filter has
been applied (fourth-order
Butterworth filter). Solid lines
are T=1C contours. c–d
Respectively the along- and
cross-shore velocities measured
by the ADCP over the slope.
The 25-h low-pass filter has also
been applied on both current
components. The vertical axis
for the three last panels is the
height above bottom (hab).
Dashed-boxes in each panels
correspond to the time period
presented in Fig. 3
0
1
2
3
4
5
L (m)
a
b
c
d
hab (m)
0
10
20
30
40
50
T (
°
C)
0
0.5
1
1.5
2
5
10
15
20
U (cm s1)
10
0
10
Sept./Oct.
20 21 22 23 24 25 26 27 28 29 30 01 02 03 04 05 06 07 08 09 10 11 12
5
10
15
20
V (cm s1)
5
0
5
The CIL exhibited large (>10 m) vertical displacements and
temperature fluctuations on weekly periods, and sometimes
even disappeared for a few days before reappearing later on.
The origin of these fluctuations is not known and they may
originate from horizontal advection of CIL inhomogeneities
associated with changes in low-frequency circulation as
suggested by panels cand d. In the along-shore direction
(panel c), the advection from the Gulf towards the estu-
ary was variable, with a maximum inland current of about
10 cm s1around 24 September and a maximum seaward
current of about 5 cm s1around 6 October. To a lesser
extent, currents were also variable in the cross-shore direc-
tion (panel d), with most of the subtidal advection at this
depth towards the interior of the channel, although a few
pulses towards the shore are also visible. It is, however,
difficult to draw any conclusions about these current fluc-
tuations based on such relatively short-term observations.
Possible explanations may, however, include Kelvin or other
topographic waves that could have been generated seaward
and traveled on this side of the channel. Such waves have
already been observed in the LSLE with periods of about
5–8 days for the lowest modes (Lie and El-Sabh 1983;
Mertz and Gratton 1990).
Figure 3focuses on tidal oscillations and presents a snap-
shot of a timeseries encompassing about six semi-diurnal
(M2) tidal cycles. Isotherms exhibit large oscillations at this
frequency with displacements reaching up to 40 m. Pock-
ets of warm water, up to 2 C, also appear semi-diurnally
and alternatively below and above the CIL. While the warm
waters seen above the CIL may have arisen from verti-
cal isotherm heaving, the source of the near-bottom waters
must come either from longitudinal (along-shore) or lateral
(cross-shore) advection. It will be shown in Section 4.2 that
this signal may be partly explained by an internal tide that
causes a periodic swash/backwash flow of warm, sub-CIL
water on the slope.
This semi-diurnal pattern is now examined using the
whole dataset averaged relative to the M2tidal cycle
(Fig. 4). In the along-shore direction (Fig. 4b), the cur-
rents near the bottom reverse earlier than those above, near
t0 h at the bottom compared to t1.5 h at 20 m
hab. Baroclinic forcing induced by internal tides may be
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Fig. 3 Example of a timeseries
from the mooring for
temperature (T), along- and
cross-shore velocities for a
3-day period, 27–30 September
2011. The temperatures are
10-min averaged and linearly
interpolated between each
thermistors, while the velocities
are 10-min averaged and raw in
the vertical (0.5 m). Thick solid
lines in aare T=1C contours
while thin lines are T=1.25
and 1.75 C. High tides (dashed-
lines) and low tides (dashed-dot
lines) are also identified in all
panels for reference
hab (m)
0
5
10
15
20
25
30
35
40
45
50
T(
°
C)
0
0.5
1
1.5
2
0
5
10
15
20
u (cm s1)
20
0
20
27Sep2011 28Sep2011 29Sep2011 30Sep2011
0
5
10
15
20
v (cm s1)
10
0
10
a
b
c
responsible for such a lag. The mean velocity profile in this
direction exhibits a log-type profile, typical of a flow above
a rigid bottom, with about 5 cm s1in the upstream direc-
tion at 20 m, decreasing towards 0 cm s1at the bottom. In
the cross-shore direction (Fig. 4c), upslope currents occur
during the flood and the early ebb for flow above 15 m hab.
Again, over the averaged M2cycle, it is possible to see that
the upslope flow arises in successive pulses as shown in
Fig. 3. The mean velocity profile of the flow over the moor-
ing duration is toward the south shore (downslope) at about
1 cm s1. The CIL also disappears during the averaged M2
cycle. This can also be seen in Fig. 3when the CIL thick-
ness decreases and sometimes disappears. The reason for
this behavior will be examined in the next subsection.
Spectral analysis reveals that although most of the vari-
ance in temperature and along- and cross-shore velocities is
at the M2frequency, higher harmonics are also present in
all fields (Fig. 5ab). To distinguish between currents in the
bottom boundary layer and above (BBL thickness is esti-
mated to be about 10-m thick later in the study, e.g., Fig. 9),
spectral analyses were performed for different depth ranges
(0–10 and 10–20 m hab). For both depth ranges, the M2
variance level largely dominated the along-shore velocities
spectra (black curves), generally by two orders of magni-
tude above the second most important harmonic (M4). The
cross-shore velocities spectra (blue curves) are, however,
only slightly dominated by M2. For example, the variance
levels in near bottom cross-shore velocities (Fig. 5a, blue
line) is nearly as high at M6than at M2(about a two-fold
change) and variance at M8is nearly as high as at M4. For
the 10–20 m depth range, variance level at M4, M6, and M8
are almost equal and less than an order of magnitude lower
than M2(Fig. 5b, blue line). This reveals that the higher
harmonics are relatively more important for vcompared
to u, consistent with the observation of successive pulses
in the cross-shore velocities discussed above and visible in
Figs. 3c and 4c
It is not surprising that uspectra are dominated by M2
considering the importance of the barotropic semi-diurnal
tide for the LSLE (Godin 1979; El-Sabh 1979; Saucier and
Chass´e 2000). The fact that the energy of higher harmonics
is different between uand vraises the hypothesis that forc-
ings responsible for the along- and cross-shore motions at
our sampling site may be different. Other than the barotropic
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Fig. 4 Mooring conditions
relative to the M2tide cycle. All
fields have been averaged in
15-min classes relative to the
high tide. The vertical axis is the
height above bottom (hab). a
Temperature field, with
isotherms 1 C and 1.3C
(black lines) added for visual
reference. b,c, along- and
cross-shore velocities, with
0.5 m vertical bins. dBase-10
log of the mean shear S2. Note
that panel aspans 50 m on the
vertical while others span only
25 m. Left side panels in bcd are
the time-averaged profiles
a
0
10
20
30
40
50
T(
°
C)
0
0.5
1
1.5
2
b
u (cm s1)
20
0
20
c
v (cm s1)
5
0
5
time to hightide (hour)
d
54321012345
log(S2 (s2))
3.6
3.4
3.2
5 0
0
10
20
321 0
0
10
20
hab (m)
3.6 3.4 3.2
0
10
20
tides, one mechanism that could drive motions at tidal fre-
quencies are internal tides. Their role as the main driver
for cross-shore velocities inducing vertical motions over the
sloping boundary will be addressed in Section 4.2.
Such tidal flows over a rigid bottom induce shear in the
water column by friction with the seafloor. This shear S2
is captured by the mooring and, as expected, is higher within
the 10-m thick bottom layer, with intensification roughly at
the end of both the flood and the ebb (Fig. 4d). Spectral
analysis of the shear at two different depth ranges shows
that it is modulated by various tidal harmonics (Fig. 5).
Between 10 and 20 m hab, the total shear (S2, magenta) is
M2-dominated, with a major contribution from along-shore
shear (S2
u, black). Higher harmonics are also present in the
total shear, but the cross-shore component of the shear (S2
v,
blue) dominates the signal at M4, M6, and M8. Shear vari-
ance is greater for 0–10 m compared to 10–20 m, although
variance in current velocities are similar for both depth
ranges (Fig. 5ab). Contribution to the shear by the along-
shore component of the velocity S2
uis dominant over S2
v
in the 0–10 m range, with S2
uvariance at M2and M4being
the most important harmonics.
4.2 A model for the propagation of internal tides
The mooring deployed on the north shore of the LSLE
shows, at a semi-diurnal time period and at higher fre-
quencies, successive upslope and downslope movements,
associated with cross-shore velocities. The barotropic radius
of deformation (R=gH
f500 km, using H=300 m
as the channel depth, gthe gravitational acceleration and f
the Coriolis parameter) is many times larger than the chan-
nel width (W36 km). This implies that the cross-shore
velocities cannot be generated by a geostrophic adjustment
of the barotropic tide entering the channel, as previously
demonstrated by Forrester (1970). In some circumstances,
however, the interaction of the barotropic tidal wave with
coastlines irregularities can lead to barotropic Poincar´e
waves which have cross-shore velocities (Taylor 1921).
To examine whether internal tides can explain the
observed velocity and temperature fields, we revisit the
study of Forrester (1974) who described the semi-diurnal
internal tide in the LSLE as being mainly a progressive
Poincar´e-type wave in the second vertical mode and first
horizontal mode. As shown in Forrester (1974), vertical
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Fig. 5 Power spectrum density
(PSD) for temperature, cross-
shore (u), and along-shore (v)
velocities, vertically averaged
over the depth range 0–10 m (a)
and 10–20 m (b) above the
seabed. c–d Power spectrum
density for the total shear (S2),
along-shore (S2
u=u
z2
) and
cross-shore shear (S2
v=v
z2)
for the same depth ranges. The
frequency is in cycle per day
(cpd). Tidal harmonics M2, M4
,M6, and M8have been added
for reference (vertical dashed-
lines). The choice of the window
used for PSD calculations
(Hanning window of 2.2 days)
makes the inertial frequency f
difficult to distinguish from M2
mode-1 is not allowed in the LSLE because the channel
width at the generation site is too narrow. For comparison
with mooring observations, this model is setup for an ide-
alized infinite rectangular channel in the x-direction, with
depth H=300 m and width W=36 km. Note that
Forrester (1974) used W= 25 km, whereas we choose
W= 36 km a width more suitable to the Rimouski section.
This channel width includes the sloping boundary where
the mooring is located, but excludes shallower shelves with
depth <40 m on either side of the channel.
Vertical displacement ηand velocities uand vfor a
Poincar´e wave of vertical mode-nand horizontal mode-m
are given by (see Forrester 1974 Eq. 6):
η(x, y , z, t) =sin λyσ λ
κfcos λyη0(z) cos(σtκx)
u(x, y , z, t) =σ
κsin λyλ
fσ2f2
κ2+λ2cos λydη0(z)
dz ×
cos(σtκx)
v(x , y, z, t) =f2κ2+σ2λ2
fκ(κ2+λ2)sin λydη0(z)
dz sin(σtκx ). (4)
Here, σis the frequency of the wave, taken as the M2
frequency σ=1.4053 ×104s1and fis the Corio-
lis parameter. Note that our x-axis is positive downstream,
opposite to Forrester’s convention but consistent with the
coordinate system of Fig. 1. The z-axis is positive down-
ward and y= 0 corresponds to the southern boundary of the
rectangular channel. Wavenumbers κand λ, respectively, in
the x- and y-directions are related through the dispersion
relation of Poincar´e waves:
σ2=f2+c2
nκ2
nm +λ2
m,(5)
where cnis the mode-dependent phase velocity of the wave
that will be determined later (see Eq. A12 in the Appendix).
Equation 5indicates that a necessary condition for Poincar´e
waves to exist is that σ> f . Because the wave is bound
by side walls in the y-direction, λm=mπ
Wfor the mth
horizontal mode of oscillation.
In order to use Eq. 4, the modal vertical displacement
structure η0(z) is needed. To do this, we followed Forrester
(1974) and considered an idealized horizontally uniform
background density stratification given by an exponential
profile of the form:
ρ=ρred
z+h.(6)
Here, ρr=1027.5 kg m3,d= 0.0924 m, and h= 15.4 m.
This represents a best fit to 198 CTD casts obtained in prox-
imity of the mooring during the deployment period (Fig. 6a,
gray lines). For all 1-m bins of the observed mean profile,
the relative error with the fit is at most 0.03 %.
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Fig. 6 Vertical density structure of the LSLE at the sampling section
and predicted vertical displacement of the internal tide. aAverage den-
sity profiles (thick lines) at the center of the channel (black) and at the
mooring site (gray) during mooring deployment period. The thin lines
are the exponential fits (Eq. 6) of both profiles, respectively. bVerti-
cal mode-2 for vertical displacement of isopycnals obtained from the
exponential fits of panel a
As shown by Forrester (1974) and re-derived here in
the Appendix, such analytical density profile allows the
following vertical structure for isopycnals displacement:
η0(z) =ηnz
h+11/2
sin ln z
h+1
ln H
h+1nπ.(7)
where ηn=3.9 m is an arbitrary scaling factor chosen to
approximately match the observed isotherms displacements.
The demonstration to obtained this structure is provided in
the Appendix. The vertical structure η0for the mooring site
is given in Fig. 6b (gray line).
Note that it is also possible to find the vertical modal
structure η0by numerically solving the Poincar´e waves
eigenvalue problem (Eq. A1), but in this case, a full-depth
(i.e., 300 m) density profile would be needed. Here, the
exponential coefficients were obtained by least square min-
imization of profiles not deeper than 110 m, but the
analytical expression was extended to 300 m, the depth of
the channel for this model (Fig. 6a, thin-gray line). Since the
stratification evolves seasonally and spatially in the LSLE,
this choice was the best trade-off to obtain a full depth
profile that best matches the surface stratification at our
sampling site. The use of a mean profile from the center
of the channel during the time of our experiment (Fig. 6a,
black lines) would have lead to a node position for vertical
displacement at 71 m instead of 54 m (Fig. 6b, black line)
which would not compare favorably with our observations.
Given the vertical displacement ηat any location and
time, the temperature field T (x , y, z, t ) can be estimated as
T (x, y, z, t) =T0(z) ηd T0
dz ,(8)
where T0(z) is the background, horizontally uniform, and
time-invariant temperature profile. This background tem-
perature profile corresponds to the mean temperature profile
sampled in proximity of the mooring during the deployment
period for the 0–80-m depth range. For illustration purposes,
the temperature profile was linearly interpolated below 80 m
to reach 5 C at 300 m, the approximate climatological
value. Since the temperature is used here as a tracer, this has
no effect on the dynamics. This simplified model provides
a framework from which the observed currents and tem-
perature signals can be interpreted. For the purpose of this
study, we limit our analysis to the cross-section correspond-
ing to the Rimouski section. Since the solution is periodic,
we assume x= 0 at the Rimouski section.
The evolution of the temperature field given by Eq. 8
over a semi-diurnal period at the location of the numerical
domain equivalent to the mooring site is given in Fig. 7.
Comparison between this figure and the first three panels of
Fig. 4shows qualitative similarities for Tand v. Modeled
Fig. 7 Predicted temperature (T), along- (u) and cross-shore (v)
velocities evolution during a M2tide cycle for an idealized mode-2
Poincar´e internal tide (Eqs. 4and 8) for approximate mooring location
(y= 33.9 km) and its depth span. For better comparison with Fig. 4, the
left-hand side vertical axis is z=z0z, where z0=83 m is the total
depth at mooring location. The horizontal axis also starts at φ=π
4
instead φ=0 for the same reason. The water column depth zis pro-
vided as the right-hand vertical axis of the figure. Isotherms T=1C
and T=1.3C have also been added in panel a(black lines)
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along-shore velocities uare weaker and not in phase with
those observed (note the different colorscale used for u), but
this is explained by the fact that the observed along-shore
velocities are dominated by the barotropic tide. Although
this calculation relies on idealized bathymetric and stratifi-
cation conditions, the resemblance between predicted and
observed cross-shore velocity amplitudes and patterns sup-
ports the idea that these are at least partly due to the
transverse component of the Poincar´e internal tide. This
model also suggests that the observed disappearance of the
CIL during an average M2cycle (Fig. 4) is the result of the
pinching of the CIL by the internal tide at a vertical node
(Fig. 7). The interaction between the internal tide currents
and the sloping boundary may also affect the temperature
evolution and may explain why the CIL often disappears,
e.g., advected away from the mooring.
Only internal tides at M2frequency were modeled here,
although M4, M6, and M8harmonics are also observed in
cross-shore velocities (Fig. 5a, b). These may be responsi-
ble for pulses in cross-shore velocities of Figs. 3c and 4c.
Wang et al. (1991) suggested that during its propagation
towards the Gulf, the energy of the semi-diurnal internal
tide rapidly decays and the relative importance of the higher
harmonics becomes greater, leading to variance levels at
M4, M6, and M8nearly as high as at M2in the cross-shore
direction. The physical mechanisms that could explain this
behavior are unclear. One possibility could be that these
higher harmonics are locally generated by the non-linear
Fig. 8 Turbulence versus water
column stability parameters as a
function of time and depth (m)
in proximity of the mooring on
September 22, 2011, measured
from a drifting boat
(repositioned at 16:13). a
Dissipation rate of turbulent
kinetic energy (). bBackground
buoyancy frequency squared in
4-m bins (N2). cBackground
shear squared in 4-m bins (S2).
d4-m scale Richardson number
(Ri). Black lines in all panels
indicate isopycnals. Magenta
lines in panels aand bindicate
regions near the bottom where
lo>κ˜z(see Section 5.3)
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interaction of the internal tide with the topography near
the mooring. Higher harmonics in the along-shore direc-
tion are also present, but are less important relative to the
variance at M2frequency, likely reflecting the importance
of the semi-diurnal barotropic tide in the LSLE.
4.3 Mean turbulent quantities
An example of near bottom dissipation sampled by the VMP
is shown in Fig. 8a, representing about 7 h of consecu-
tive sampling, i.e., our longest timeseries near the mooring
location. Each of the casts realized on this occasion hit the
bottom at depths varying between 74 and 91 m. Since the
boat was slowly drifting towards shallower water, it was
repositioned near 16:13 UTC. Figure 8also presents the
buoyancy frequency squared N2, averaged in 4-m bins to
match the shear vertical resolution computed from the out-
board ADCP S2. The latter was 1-h filtered and combined
to the buoyancy frequency to compute gradient Richard-
son number Ri =N2
S2that is presented here as tanh(Ri )
to better highlight regions below the threshold Ri =1
4
(orange-red colors) where shear instabilities are expected
to occur (Miles 1961; Howard 1961). This is useful to bet-
ter visualize unstable regions since tanh(Ri) Ri for
Ri < 0.5 and tanh Ri|Ri+=1.
The dissipation is generally patchy, with enhanced turbu-
lence levels both near the seabed and in the interior. Near the
seabed, a notable feature is the high dissipation rate found
between 13:00 and 15:00, a period corresponding to the end
of flood (high tide at 14:31 UTC). This period and location
correspond to high shear and low Ri. Note that although
turbulence is high, the bottom boundary layer maintains its
stratification N2>105s2. Further away from the bot-
tom, turbulent layers a few meters thick that can last for
hours are found. These are generally aligned with bands of
high shear and low Ri . Such bands of high dissipation show
strong similarities with that found in the Baltic Sea, which
were attributed to shear caused by sub-inertial internal wave
motions (e.g., van der Lee and Umlauf 2011). The possi-
ble relation between shear, stratification, and dissipation is
examined in Section 5.3.
We summarized all similar sorties in Fig. 9, where 322
VMP casts and corresponding (simultaneous) velocity and
shear profiles from the outboard ADCP are presented. High-
est shear (Fig. 9b, black curves) is found in the bottom 10 m
of the water column and corresponds to a rapid decrease in
the mean velocity U=u2+v2(Fig. 9a). On the other
hand, the stratification N2(Fig. 9b, gray curves) decreases
steadily from about 50 m to the bottom, except in the bottom
5 m where it slightly increases. Ri decreases quasi-linearly
from about 50 to 10 m hab (Fig. 9c). Between 10 and 5 m,
Fig. 9 Averaged quantities of our 322 VMP casts (solid lines).
Averaged profiles when considering only flood (dashed) and ebb
(dot-dashed) are also presented. aVelocity profiles U=u2+v2
from the ADCP deployed outboard, corresponding to VMP casts. b
Shear (S2,black lines) calculated with velocity profiles from outboard
ADCP, and stratification (N2,gray lines) from VMP casts. cRichard-
son number (Ri =N2
S2) calculated from the ratio of mean profiles
of panel b.dDissipation rate of TKE when using all available bins
(thick black lines) and bins when the size of overturns is limited by the
stratification, e.g., when lo<κ˜z(thin gray line). Also on this panel,
the dissipation when the size of overturns is not limited by the stratifi-
cation (lo>κ˜z,thick gray line) and the dissipation inferred from near
bottom velocities using the log-law scaling presented in Section 5.3
(˜=u3
κ˜z,dashed-gray line). eTurbulent diffusivity calculated using
a constant (Γ=0.2, black lines) and variable (Eq. 3,gray lines)
flux coefficient. Except U, averaged profiles are calculated assuming
log-normal distribution
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Ri decreases more rapidly driven by the increasing shear
and falls below the threshold Ri =1
4(vertical dashed-line).
In the bottom 5 m, Ri remains almost constant and below
the threshold.
The dissipation rate of TKE () presented in
Fig. 9d (black lines) increases toward the bottom of
the water column. Flood and ebb averaged profiles
are more or less the same until below 10 m hab
where flood 2.8(1.9,3.9)×107W kg1exceeds
ebb 0.72(0.53,0.98)×107W kg1by about a four-
fold change on average. Here, numbers in parentheses are
the bootstrapped 95 % confidence interval on the mean
value and overlines refer to a vertical average of the mean
profile in the 0–10 m hab depth range. On average, the
enhanced dissipation near the seabed during the flood is
consistent with the snapshot presented in Fig. 8. The aver-
age dissipation rate in the bottom 10 m over all casts is
10 m =1.6(1.2,2.0)×107W kg1, an order of magni-
tude greater than that measured far from the boundaries and
reported in Cyr et al. (2011).
Mean diffusivity profiles are calculated here using both
constant (Γ=0.2, black lines) and variable (Eq. 3, gray
lines) mixing efficiencies. Using Γ=0.2 , mean diffusiv-
ity in the bottom 10 m hab gives Kflood =11(6.7,18)×
104m2s1,Kebb =2.5(1.6,3.8)×104m2s1and
K10 m =6.0(4.1,8.5)×104m2s1. When calculated
using the Shih et al. (2005) parametrization, the average dif-
fusivity for the bottom 10 m is KShih =6.5(5.6,7.6)×
105m2s1, i.e., nearly an order of magnitude lower than
when using Γ=0.2. Previous studies have suggested such
substantial reduction of the mixing efficiency (Γ0.2) for
energetic mixing near bottoms having slopes similar to that
of our sampling site (Umlauf and Burchard 2011; Becherer
and Umlauf 2011). However, these studies also predict con-
siderably reduced stratification above the seafloor which
is not the case in the present observations (Fig. 9b sug-
gests a slight increase of the stratification in the bottom
5 m). Average diffusivity calculated with the Shih et al.
(2005) parametrization is also inconsistent with the near
bottom diffusivities inferred by inverse modeling in this area
(Cyr et al. 2011).
5 Discussion
5.1 CIL behavior in response to internal tides
The study suggests that during the mooring deployment, the
node for vertical displacement was located near 25–30 m
hab, i.e., at CIL depth (Fig. 4). Our best fit on the density
profile yields a node in the solution of vertical displace-
ment (η0, Eq. 7) at z= 54 m, i.e., 29 m hab at mooring
site (Fig. 6b, gray line), thus supporting the idea that the
pinching of the isotherms at this depth is the reason
why the CIL disappears at some phases of the M2tide
cycle.
Our study also highlights that this node position is highly
variable depending on near-surface stratification. Using the
density profile measured at the center of the channel instead
of near the boundary to compute the second vertical modal
structure would displace the node down by nearly 20 m
(Fig. 6b, black line). With such horizontally inhomoge-
neous stratification, internal tides generated at the head of
the Laurentian channel are thus spatially modulated dur-
ing their propagation out of the estuary. This changing
vertical structure thus makes any generalization concern-
ing their behavior (node position, current amplitudes, etc.)
difficult and caution should be taken in interpreting these
results.
Cross-shore currents are also associated with internal
tides. In our model, however, they do not interact with the
real topography. In the real case of a sloping boundary, these
currents could generate upslope and downslope currents.
This may explain the asymmetry (maximum displacement
not in phase at each depth) that exists in Fig. 4a compared
to Fig. 7a. Although uand vvelocities are nearly in phase
(upslope flow during the flood), this is fortuitous since inter-
nal tides have a wavelength in the propagation direction
many times smaller than the barotropic tides. Depending
on the distance from the generation site, the current rever-
sals of internal tides do not necessarily occur in phase with
the reversal of the barotropic tide that generated it. At the
mooring site, the lag between barotropic high tide and cross-
shore current reversal (driven by internal tides) is about 1.5 h
(Fig. 4), about equivalent to the phase shift applied in Fig. 7
for better visual comparison (φ=π
41.5 h for the M2
period).
Internal tides in the LSLE thus impact, at semi-diurnal
and higher frequencies, the velocity, salinity, temperature,
and other physicochemical property distribution. In prepa-
ration to field programs, care should be taken to not under-
sample in time the water column properties that are subject
to large variations due to such isopycnals heaving. For
example, a CIL index based on the cold water volume
(Galbraith 2006) is used in annual reports on the physical
oceanographic conditions of the Gulf of St. Lawrence (e.g.,
Galbraith et al. 2014). When based on a single profile, esti-
mates that use the CIL thickness may be not representative
of the mean conditions, depending on which phase of the
isotherms heaving it has been realized.
5.2 Boundary mixing in the LSLE
From about 150 casts (not necessarily above the sloping
boundary), Cyr et al. (2011) reported near bottom diffu-
sivity to be Kb=3.3(2.1,4.8)×104m2s1. With such
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a diffusivity, boundary mixing was estimated to account
for about one third of the mixing budget in the LSLE.
When analyzed in terms of dissipation, this corresponded
to b=1.2(1.0,1.4)×107W kg1(values not reported
in Cry et al. 2011). In the present study, a more extensive
sampling above the sloping bottom reveals that the average
dissipation and diffusivity in the bottom 10 m are 10 m =
1.6(1.2,2.0)×107W kg1and K10 m =6.0(4.1,8.5)×
104m2s1(Section 4.3), thus higher than the results of
Cyr et al. (2011).
The study, however, supports the findings of Cyr et al.
(2011) that boundary mixing is significant at the scale of
the LSLE and possibly the Gulf of St. Lawrence. Using
a scaling for the effective diffusivity at the basin scale
(Ke, Cyr et al. 2011, Eq. 5with updates from this study),
we suggest Ke=4.1×105m2s1and reassess that
boundary mixing can account for about 30–40 % of this
value.
Mean profiles reported in Fig. 9are also informative of
the nature of turbulent processes encountered in the LSLE.
For certain shallow highly stratified or partially mixed
estuaries, one may expect that most of the dissipation is
determined by bottom stress and stress in the pycnocline
(e.g., Geyer and Smith, 1987; Geyer et al., 2000,2010). In
these estuaries, the stratification varies within a broad range
of values between ebb and flood conditions with often very
weak stratification during strongest tidal flow (e.g., Nepf
and Geyer 1996; Peters 1997; Geyer et al. 2000, Kay 2003).
The LSLE does not behave such as these estuaries since
even in the near bottom part of the water column the strati-
fication remains nearly constant between the ebb and flood
(Fig. 9b). Although near bottom dissipation, , is modu-
lated by the semi-diurnal tide cycle (by a fourfold change,
Section 4.3), the difference at each depth between the flood
and ebb mean stratification profiles is always less than 1 %.
In fact, with a mean stratification near N102s1and
dissipation rate in the [108,107]W kg1range,
turbulence in the LSLE falls within the continental shelf tur-
bulence definition, following the classification of oceanic
and estuarine turbulence by Geyer et al. (2008) (see their
Fig. 1). Mixing mechanisms likely to be encountered in
the LSLE are thus those usually present at the continental
slope, including shear instabilities of various origin, bottom
friction, and internal wave induced mixing.
5.3 Mixing mechanisms and forcings
Our observations suggest that bottom and interior mixing
processes are at work at our sampling location. The former
is suggested by the high dissipation rates found near the bot-
tom, while the latter is suggested by the higher shear and
dissipation bands found in the interior of the water column
(Figs. 8and 9). These two regions will be discussed next in
an attempt to identify mixing mechanisms at work and their
origin (forcings).
5.3.1 Bottom boundary region
In this area subject to intense tidal currents, mixing by bot-
tom shear stress resulting from the friction of the flow over
the bottom may be expected to occur. For an steady homoge-
neous flow, the dissipation driven by bottom friction should
follow a log-law scaling, commonly referred to as the law
of the wall:˜=u3
κ˜z. Here, κ=0.41 is the von K´arm ´an con-
stant, ˜zthe distance from the bottom and u=CdUbthe
friction velocity that depends on a constant drag coefficient
(Cd) and the near bottom velocity Ub(see Walter et al. 2012
for example).
Since this theory is suitable for unstratified water, we first
identified near bottom profiles where buoyancy effects were
not expected to affect overturning in the bottom boundary
layer (BBL). This condition is expected to hold when the
Ozmidov scale (lo=
N31
2, a length-scale for the size of
overturns limited by stratification) is larger than the scale of
the overturns limited by their distance to the bottom (l=κ˜z,
the length-scale that appears in the law-of-the-wall). This
condition can be written lo>κ˜z(see also, for example,
Perlin et al. 2005; van der Lee and Umlauf 2011).
The result of this condition for our sampling on 22
September 2011 is highlighted by the magenta lines in
Fig. 8. Such weaker stratification near the bottom was found
in about 65 % of the 322 VMP casts and were not linked
to any particular phase of the M2tidal cycle (not shown).
Moreover, for 90 % of the time, the weakly stratified BBLs
identified this way were 2 m, and were never thicker than
6 m. These weak stratification conditions, however, drive
most of the near bottom dissipation as suggested by the dif-
ference between the thick and the thin gray lines in Fig. 9d,
which are, respectively, the average of low stratification bins
and the averaged profile without them. Above 6 m hab
(and most of the time above 2 m hab), the stratification
will prevent growing turbulence from the bottom frictional
layer.
Moreover, the dissipation profile inferred in the bottom
6 m using the above log-law scaling (Fig. 9d, dashed-gray
line) is comparable, in magnitude, to the dissipation pro-
file observed during periods of low stratification (thick-solid
gray line). Here, the log-law scaling was calculated using
Cd=3×103(Soulsby 1997) and Ub=U2m, the velocity
measured by the moored ADCP at 2 m hab and 15-min fil-
tered to reduce the error on the measurements. Note that we
used U2m rather than the commonly used velocity at 1 m hab
to avoid the side-lobe effects of the ADCP measurements
near the seabed. The use of different drag coefficients would
not significantly affect this comparison because using Cd=
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[15] × 103(range of values commonly found in the lit-
erature) leads approximately to a twofold change on w al l .
The two profiles above also compare favorably when look-
ing at their averaged values, which are lo>κ˜z=7.2×
107W kg1and wal l =8.1×107W kg1, respectively,
for the low stratified BBL and inferred from the log-scaling.
The fact that the dissipation inferred from near bottom
velocities scales relatively well with the measured dissipa-
tion when the stratification is low suggests that most of the
dissipation in the bottom 6 m of the water column are driven
by bottom shear stress. This is also suggested by the fact that
within this depth range, S2and N2(and thus Ri ) are approx-
imately constant between flood and ebb, implying that shear
instabilities cannot account for the difference between flood
and ebb. In the same depth range, however, the mean veloc-
ity profile is, however, shifted towards greater values during
the flood compared to the ebb, implying greater kinetic
energy input to be dissipated by bottom friction. Because
shear in the along-shore direction largely dominates the
shear spectrum in the 0–10 m hab depth range (Fig. 5),
we may hypothesize that the barotropic tidal currents are
the main drivers for bottom shear stress mixing, although
internal tides also generate near bottom shear. Conditions
favorable to bottom shear stress occur in about 65 % of
our VMP casts, but is generally limited to the bottom 2 m
hab. Elsewhere, the turbulence generated by bottom fric-
tion is likely suppressed by the stratification as suggested
by the lower dissipation when ignoring bins having low
stratification (thin gray line in Fig. 9d).
In counterpart, other mechanisms besides bottom stress
must explain the approximately exponential increase of the
dissipation from about 25 to 5 m hab (Fig. 9d). Such an
increase, combined with the fact that the BBL is mostly
stratified, suggests internal waves scattering (or bottom
wave generation) as a possible mixing mechanism responsi-
ble for this near bottom mixing enhancement (Garrett et al.
1993; Toole et al. 1994; Slinn and Riley 1996; St Laurent
2002). This mechanism was also recently summarized by
Gregg et al. (2012) for mixing above a continental slope.
5.3.2 Interior mixing
The localized bands of enhanced turbulence presented in
Fig. 8seems to correspond to bands of lower Richardson
number, suggesting that shear instabilities are at work in
the interior of the water column. These may be induced
by internal shear or high-frequency internal waves locally-
generated by the Poincar´e internal wave (Bouffard et al.
2012). To examine a possible systematic relation between
stratification, shear, and dissipation, we plotted 4-m resolu-
tion bin of as function of N2and S2in a manner similar to
MacKinnon and Gregg (2003), Carter et al. (2005), Palmer
et al. (2008), and Schafstall et al. (2010), van der Lee and
Umlauf 2011 and others (Fig. 10a). For this exercise, we
ignored bins below 10 m hab, the region of the water
column most likely affected by boundary processes (see
corresponding shear enhancement in Fig. 9b). Similarly, to
ignore turbulence in the surface layer affected by atmo-
spheric forcing, we also discarded surface first 5 m, a range
considered conservative since observations clearly do not
show a mixed layer near the surface (Fig. 8b). The resulting
figure is compared with the MacKinnon and Gregg (2003)
parametrization, hereafter MG (Fig. 10b), a parametrization
specifically designed to model mixing by wave-wave inter-
actions in the coastal ocean, and favorably compared with
observations from the New England Shelf (MacKinnon and
Gregg 2003;2005), the Celtic Sea (Palmer et al. 2008), and
the Baltic Sea (van der Lee and Umlauf 2011). The equation
for this parametrization is:
MG =0N
N0S
S0,(9)
where N0=S0=3 cph (MacKinnon and Gregg 2003)
and 0=1.0×108W kg1, chosen here so that the
parametrization average matches the average of the obser-
vations.
Here, observations of and the predicted MG do not
visually match well, although likely also increases with
increasing N2and S2as suggested by the parametrization
(Fig. 10a). This is supported by plotting as function of
N2and S2alone (Figs. 10c, d, shaded areas). Similar aver-
ages of MG (Figs. 10c, d, dashed-lines) suggest, however,
that the dissipation increase with N2and S2is slightly over-
estimated by the parametrization. Such poor agreement of
in the N2-S2space but good functional dependence of
with increasing N2and S2was also obtained by Carter
et al. (2005) and Schafstall et al. (2010) in regions where
mixing is partly driven by high wavenumber and non-
linear internal waves. Carter et al. (2005) recalled that while
the MacKinnon and Gregg (2003) parametrization was
developed for stable wave-wave interactions, the presence
of nearby topography may induce internal wave scatter-
ing (energy transfer to higher modes) that is not taken into
account by the parametrization. Note that internal wave
scattering was also hypothesized in the preceding sub-
section to explain the gradual increase of dissipation as the
bottom is approached in the 0-25 m hab depth range.
Neither taken into account by the parametrization is
the non-linear energy transfer from vertical mode-2 of the
Poincar´e wave into higher harmonics (M4, M6, M8) sug-
gested from the shear spectrum in the 10–20 m hab range,
particularly in the cross-shore direction (Fig. 5d). These
higher harmonics may be generated by interaction with
the nearby topography. Finally, our estimation of the scal-
ing parameter 0=1.0×108W kg1is about 15 times
higher than that used in the original MacKinnon and Gregg
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Fig. 10 Dissipation rates of
turbulent kinetic energy as a
function of the buoyancy
frequency squared (N2) and of
the shear squared (S2). a
Observations from all 322
profiles with bottom 10 m hab
and top 5 m removed. The solid
and dashed-lines are,
respectively, Ri =1 and
Ri =1
4.bSame as a, for
MacKinnon and Gregg (2003)
scaling MG (Eq. 9). c–d
Respectively, the vertical and
horizontal averages of the two
panels above to highlight the
effect of the buoyancy frequency
and the shear on dissipation. The
shaded areas are the
bootstrapped 95 % confidence
interval on observations
(panel a) while the dashed-black
lines are the averages of the
predicted MG (panel b)
(2003) parametrization, also suggesting that some underly-
ing physics may be missing for a direct application to a more
energetic area such as the LSLE.
6 Conclusion
In a recent study, Cyr et al. (2011) concluded that although
not dominant, boundary mixing can contribute significantly
to the erosion of the Gulf of St. Lawrence CIL. In the
conclusion of that study, questions were raised concerning
possible boundary mixing mechanisms. This partly moti-
vated the deployment of the mooring at station N080, i.e.,
where the CIL intersects the sloping bottom. Mooring obser-
vations were completed with 322 VMP turbulence profiles
down to the seabed.
CIL behavior at the slope has been depicted as alter-
nating swashes/backwashes of the layer on the slop-
ing boundary at a semi-diurnal frequency, with superim-
posed higher harmonics. At the mooring location, the CIL
also thickens and shrinks (and sometimes disappears) at
semi-diurnal and higher frequencies. This behavior is part of
the three-dimensional structure of internal tides generated at
the head of the Laurentian channel that propagate out of the
estuary. During their propagation, internal tides may pos-
sibly be degenerated by interactions with the topography,
generating higher harmonics. To date, studies focusing on
internal tides in the LSLE have been limited to scarce obser-
vations and idealized models, and the region still lacks
a detailed description of the propagation of these tides.
This description is, however, difficult because of the com-
plex bathymetry and changing water stratification properties
along the channel.
Observations suggest that the analysis of turbulent mix-
ing mechanisms at the sampling site can be divided into the
near-bottom and a water column interior area. Near-bottom
turbulence increase with decreasing hab is partly driven by
shear stress caused by the friction of the barotropic tidal
currents. When currents were maximum, i.e., during flood,
the dissipation rate of TKE was approximately four times
higher than during ebb. Such strong turbulence occurred
in about 65 % of our profiles and corresponded to periods
Author's
personal copy
Ocean Dynamics
when the maximum size of overturns in the BBL was not
limited by stratification. The portion of the BBL subject to
such a mechanism never exceeded 6 m hab and was gener-
ally limited to the bottom 2 m hab. Below about 25 m hab
but above the weakly stratified BBL, the dissipation also
increased with decreasing hab, albeit to a lesser extent as
the bottom was approached. Since the stratification likely
suppresses turbulence growth from bottom stress in this por-
tion of the water column, internal wave scattering may be
responsible for this increase.
Dissipation rates were also compared with stratification
and shear conditions in order to identify if the observed
internal tides may partly explain the band-like shear and
high dissipation rates in the interior of the water col-
umn. The poor agreement between the observations and
the MacKinnon and Gregg (2003) parametrization sug-
gests that mechanisms other than stable wave-wave interac-
tions must be at work. Since this parametrization does not
account for nearby topography, the presence of the sloping
boundary at our observation site may explain the discrep-
ancies. It would be interesting, however, to compare this
parametrization with observations from the interior of the
basin (far from boundaries) where, as our results reassess,
about two-third of the mixing budget of the LSLE take
place.
Acknowledgements This work was funded by “Le Fonds de
recherche du Qu´ebec - Nature et technologies,” the Natural Sciences
and Engineering Research Council of Canada, the Canada Foundation
for Innovation and Fisheries and Oceans Canada and is a contribu-
tion to the scientific program of Qu´ebec-Oc´ean. The authors would
like to thank R´emi Desmarais and Paul Nicot who were frequent crew
members during our summer sampling campaigns, Leo Maas for his
help with the derivation of the Poincar´e wave equations, and C´edric
Chavanne, Luc Rainville and two anonymous reviewers who provided
valuable comments to improve this manuscript.
Appendix: Analytical solutions for the vertical modal
structure of isopycnal displacements
In this Appendix, we re-derive the analytical expression for
the vertical modal structure of the Poincar´e wave for the
isopycnal displacements η0(z) given a analytical density
profile (Eq. 6).
A1 Problem formulation
For a certain vertical mode n,η0is the solution of the ordi-
nary differential equation (ODE) given by (e.g., Cushman-
Roisin and Beckers, 2011):
d2η0
dz2+N2σ2
c2
nη0=0,(A1)
where N2=g
ρ
∂ρ
z=gd
(z+h)2given the density profile
imposed by Eq. 6, and cnthe phase velocity that, as we
will show later, depends on the vertical mode n. If we let
ν2=gd
c2
n
, and neglecting σ2because N2>> σ2, Eq. A1
can be re-written:
d2η0
dz2+ν2
(z +h)2η0=0.(A2)
A2 Simplifications and general solution of the problem
To resolve the problem, we start by introducing two succes-
sive variable changes in order to scale the equation. We first
introduce the non-dimensional parameter ξsuch as z=ξh
(dξ=1
hdz). Then, if we let ζ=ξ+1 (dζ=dξ), the ODE
becomes:
d2η(z)
dζ2+ν2
ζ2η=0.(A3)
We now assume that the solution has the form η0(ζ)=
A(ζ)B(ζ). After applying the derivative rules, the ODE is
now:
Ad2B
dζ2+2AζdB
dζ+Aζ ζ B+ν2
ζ2AB =0
d2B
dζ2+2Aζ
A
dB
dζ+BAζ ζ
A+ν2
ζ2=0.(A4)
where subscripts to variable Astand for derivative relative
to ζ. The passage from the first to the second line of Eq. A4
was made by multiplying by 1/A.
We now choose A=ζ1/2. Knowing that:
Aζ=1
2ζ1/2,
Aζ ζ =1
4ζ3/2,
Aζ
A=1
2ζand
Aζ ζ
A=1
4ζ2,(A5)
and by multiplying Eq. A4 by ζ2, the ODE becomes:
ζ2d2B
dζ2+ζdB
dζ+Bν21
4=0.(A6)
We now introduce a new variable change s=ln(ζ)(thus
ζ=eS) which results in the following derivation rules:
ds
dζ=1
ζ=es,
d
dζ=esd
ds and
d2
dζ2=e2sd2
ds2d
ds .(A7)
Author's
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Ocean Dynamics
With this variable change, the equation is:
d2B
ds2+ν21
4B=0.(A8)
This last expression is a second-order homogeneous dif-
ferential equation with constant coefficients that can be
resolved with standard procedures (see any ODE textbook).
The characteristic equation for this equation is λ2+μ2=0,
where μ2=ν21
4. Since μ2is positive by construction
(this can be easily verified later), the characteristic equation
leads to complex roots λ= ±iμ. In this case, the analytical
solution for the variable Bhas the form:
B=C1cos(μs) +C2sin(μs), (A9)
where C1and C2are constant coefficients to be determined.
A3 Specific solutions given the boundary conditions
Recalling that η0(ζ)=A(ζ)B(ζ)and A(ζ)=ζ1/2, we can
now use the boundary conditions on η0to find the specific
solution of our problem. Because displacements are verti-
cally limited by the seafloor and the surface, the boundary
conditions are η0(z =0)=0 and η0(z =H ) =0, where H
is the total depth. Given the variables changes made in the
preceding, these boundary conditions imply B (s =0)=0
(i.e., z=0ζ=1s=0) and Bs =ln (H / h +1)=
0 (i.e., z=Hζ=H
h+1s=ln H
h+1).
The first boundary condition (at the surface) implies that
C1= 0, while the second condition implies that the argument
under the sine must be of the form μs=nπ, with n=
1,2, ..., an integer corresponding to the nth vertical mode.
Substituting s=ln H
h+1in the preceding, a necessary
condition is that:
μ=nπ
ln H
h+1.(A10)
After replacing all terms by their expressions in zand
taking into consideration these boundary conditions, Eq. A9
becomes:
η0(z) =ηnz
h+11/2
sin ln z
h+1
ln H
h+1nπ.(A11)
Note that in the last expression, C2has been replaced by
ηnfor clarity and is the parameter that carries the dimen-
sion (m) of η0. This constant parameter is determined by
fitting Eq. A11 to observations. Note also that Eq. A11 is
slightly different than the one presented in Forrester (1974)
(its Eq. 10), but by carefully adjusting the constant parame-
ters in Forrester’s equation, we can show that both equations
give the same structure.
Another consequence of the second boundary condition
(Eq. A10) is that it gives conditions on the phase velocity
(cn) of the admissible Poincar´e waves. Replacing μby its
expression in zthis equation leads to:
c2
n=gd
nπ
lnH
h+12
+1
4
.(A12)
This expression is necessary for the dispersion relation
presented in Eq. 5.
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... Avec nos hypothèses, les équations qui régissent l'évolution du fluide sont ρ 0 ∂v x ∂t + ∂p ∂x = 0 Navier-Stokes suivant x (I. 13) ρ 0 ∂v z ∂t + ∂p ∂z − ρ g = 0 Navier-Stokes suivant z (I.14) 15) ∂v x ∂x + ∂v z ∂z = 0 Conservation de la masse (I. 16) On réécrit ces équations en utilisant la fonction courant. ...
... Avec Géraldine Davis, nous avons réalisé un tel dispositif dans la grande cuve. La figure I. 15 représente les lignes de colorant obtenues. Les zones de mélange proches des parois sont générées lors de l'entrée et de la sortie de la structure soutenant les fils. ...
... La relation (II. 15) est vérifiée en tenant compte des grandes barres d'erreurs obtenus pour le calcul de − → k . Il a été observé sur plusieurs expériences indépendantes et sur des simulations numériques directes qu'une des ondes secondaires possède un spectre en k proche d'une décomposition bi-modale. ...
Thesis
Les ondes internes de gravité jouent un rôle essentiel dans la dynamique océanique. La relation de dispersion anisotrope de ces ondes conduit à des lois de réflexions qui sont différentes de celles dont nous avons l'habitude avec les ondes acoustiques ou les rayons lumineux.Dans cette thèse de doctorat, nous nous intéressons aux structures créées par ces ondes en deux dimensions puis en trois dimensions. Dans la plupart des géométries 2D, le parcours des ondes va converger vers un attracteur. Nous étudions d'abord expérimentalement, dans une géométrie trapézoïdale, l'aspect énergétique d'un de ces attracteurs d'ondes. Nous examinons ensuite expérimentalement le devenir de ces attracteurs dans des géométries tridimensionnelles. Dans certaines géométries, la réflexion des ondes conduit à un phénomène de piégeage dans un plan 2D. Ce phénomène, d'abord étudié à l'aide de tracés de rayons, a été reproduit dans une géométrie trapézoïdale ainsi que dans une géométrie de canal. Cette mise en évidence expérimentale du piégeage pourrait expliquer certaines mesures in-situ réalisées dans l'estuaire du Saint Laurent où la propagation des ondes internes est encore mal comprise.Cette thèse est enrichie par deux études expérimentales portant sur la propagation et la réflexion d'un faisceau d'ondes interne : d'une part, l'instabilité créant un courant moyen dans le cas d'un faisceau se propageant dans une géométrie tridimensionnelle et d'autrepart la génération d'ondes rétro-réfléchies lors de la réflexion sur des surfaces courbes. Les résultats novateurs que nous avons obtenus sont dans les deux cas en accord avec la théorie.
... The parameterization based on a constant mixing efficiency significantly improves the recovery of the heat budget compared to a mixing efficiency that varies with the turbulence activity index (Figure 9b). These results suggest that the experimentally defined constant mixing efficiency might still be more accurate than the parameterization relating the mixing efficiency with the turbulent activity index, as already suggested by Gregg et al. (2012) andCyr et al. (2015). Overall, these results underline the importance of diapycnal mixing for heat transfer into deeper layers of the water column and are in good agreement with previous studies (Palmer et al., 2008(Palmer et al., , 2015. ...
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... Additionally, to determine l t for weakly stratified to well-mixed regimes, the Corrsin scale L C 5ðE=S 3 Þ 1=2 is calculated, in which S represents a typical vertical profile of shear in the measurement region. The Corrsin scale determines the maximum length scale of an eddy in regimes dominated by shear (Corrsin, 1958;Smyth & Moum, 2000). Boundary effects in the water column also limit the size of turbulent eddies and are accounted for by estimating a third, geometric, length scale L G 5jzð12z=H tot Þ (Simpson & Sharples, 2012). ...
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We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, 2D parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics,emphasize the role of boundary conditions and reveal the phase shifting in the transversal direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.
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... Subsequent observations, along one side of this Channel, do show evidence of internal tides. These appear to be forced at the nearby located transverse sill at the head of the Laurentian Channel, and while initially expected to propagate down-channel, they appear to be responsible for observed transverse internal tidal motions (Cyr et al. 2015), such as expected from the refractive trapping mechanism. ...
Article
We study experimentally the propagation of internal waves in two different three-dimensional (3D) geometries, with a special emphasis on the refractive focusing due to the 3D reflection of obliquely incident internal waves on a slope. Both studies are initiated by ray tracing calculations to determine the appropriate experimental parameters. First, we consider a 3D geometry, the classical set-up to get simple, two-dimensional (2D) parallelogram-shaped attractors in which waves are forced in a direction perpendicular to a sloping bottom. Here, however, the forcing is of reduced extent in the along-slope, transverse direction. We show how the refractive focusing mechanism explains the formation of attractors over the whole width of the tank, even away from the forcing region. Direct numerical simulations confirm the dynamics, emphasize the role of boundary conditions and reveal the phase shifting in the transverse direction. Second, we consider a long and narrow tank having an inclined bottom, to simply reproduce a canal. In this case, the energy is injected in a direction parallel to the slope. Interestingly, the wave energy ends up forming 2D internal wave attractors in planes that are transverse to the initial propagation direction. This focusing mechanism prevents indefinite transmission of most of the internal wave energy along the canal.
... The Lower St. Lawrence Estuary (Eastern Canada) with its river bed essentially U-shaped transversally and longitudinally invariant over 1000 km [9] is a prototypic example. This site is remarkable since even though internal tides are known to be generated at the land-locked head of the Channel [10], surprisingly low intensity internal tides have been measured near the mouth of the Laurentian Channel, eastern Canada [11]. It is therefore important to study propagation and reflection of internal waves in such a geometry. ...
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We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew's cross justifies the introduction of an angle of propagation that allows to describe the position of the wave ray in the horizontal plane. Considering the evolution of this reflection angle for waves that repeatedly reflect off an inclined slope, a new trapping mechanism emerges that displays the tendency to align this angle with the upslope gradient. In the rather simple geometry of a translationally invariant canal, we show first that this configuration leads to trapezium-shaped attractors, very similar to what has been extensively studied in two-dimensions. However, we also establish a direct link between the trapping and the existence of two-dimensional attractors. In a second stage, considering a geometry that is not translationally invariant, closer to realistic configurations, we prove that although there are no two-dimensional attractors, one can find a structure in three-dimensional space with properties similar to internal wave attractors: a one-dimensional attracting manifold. Moreover, as this structure is unique, it should be easy to visualize in laboratory experiments since energy injected in the domain would eventually be confined to a very thin region in three-dimensional space, for which reason it is called a super-attractor.
... Diffusion-induced flows are manifested, as a rule, in the form of slope jet flows which can cause the so-called mountain, valley (Prandtl 1952) and glacier (Oerlemans and Grisogono 2002) winds, melting of icebergs (Huppert and Turner 1978), and migration of tectonic plates, as well. These flows essentially affect the global processes in the ocean Zagumennyi 2013a, 2013b), including passive substances transfer, mixing processes (Cyr et al 2015), formation of flow fine structure and self-motion of separate particles, microorganisms, plankton, etc (Allshouse et al 2010, Zagumennyi andDimitrieva 2016). ...
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Wave and vortex fine structure of unsteady stratified flows were studied numerically based on the system of fundamental equations for non-homogeneous incompressible fluid with no-slip and no-flux boundary conditions, and experimentally using high-resolution Schlieren visualization techniques. Different flow regimes, including creeping, wave and vortex ones, which are widespread in the ocean and atmosphere, were investigated in the single problem formulation, starting from the slowest diffusion-induced flows up to the fastest and unsteady ones. A classification of flow components is proposed, which contains waves, vortices, and ligaments, which manifest themselves in the form of extended interfaces with their transverse scales being determined by the dissipative properties of a fluid and the flow dynamics. Due to interrupting the molecular flux of a stratifying agent on a motionless obstacle, fine structural diffusion-induced flows are formed around the obstacle in the form of a multilevel set of vortex cells which are transformed near the edges into horizontally extended streaky structures. A moving body in a stratified fluid produces upstream disturbances, groups of attached internal waves, leading-edge vortices, and a vortex street in the wake, which coexist in the stratified flow as an organic whole and are separated with ligaments. In the unsteady vortex flow regime, the shape of the bluff body essentially affects the flow structure, determining whether it will consist of a quasi-steady chain of vortices with a quite regular vortex shedding structure, or leading-edge vortices and vortex street would evolve into a much more complex and multi-scale vortex evolution. The numerical and experimental visualizations of diffusion-induced flows, internal waves, vortex streets, and fine structural ligaments, are in a qualitative agreement with each other.
... Galbraith (2011, 2015) examined boundary mixing above the sloping bottom in the Gulf of St. Lawrence (Canada). Although turbulent dissipation in the BBL was high (the meanε ∼ 10 −7 to 10 −8 W kg −1 ), the BBL (∼10 m thick) maintained its stratification with N 2 > 10 −5 s −2 (Cyr et al., 2015). These measurements showed an approximate exponential growth of ε toward the bottom ( fig. 13 of Cyr, Bourgault, and Galbraith 2011). ...
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The application of the classical logarithmic layer model for wall-bounded shear flows to marine bottom boundary layer (BBL) usually leads to an overestimation of the friction velocity u * due possibly to the influence of form drag, stratification, and rotation of the flow vector. To gain insights on the BBL velocity scaling, acoustic Doppler current profiler (ADCP) measurements taken in the East China Sea were analyzed (a total of 270 sixteen-minute averaged velocity profiles). Single and double log-layer models, a log-wake model, and a modified log-layer (MLL) model that accounts for stratification in the upper part of the BBL (Perlin, Moum, Klymak, Levine et al. 2005) were explored. Although the first three models fit well for a majority of the profiles, the friction velocities appeared to be substantially overestimated, leading to unreasonably high drag coefficients. The friction velocity u * ml inferred from a slightly modified MLL, however, is half of that estimated using the classical log-layer assumption u * l . In a weakly stratified extended BBL, the dissipation rate ε decreases with the height from the seafloor ζ much faster than that in a homogeneous stationary BBL. This observation could be well approximated (in terms of r 2) by an exponential ε (ζ) = ε0 e –ζ/Lm or a power law decrease. The mixing length scale Lm = cLhBL , where hBL = 19–20 m is the BBL height and cL = 0.17, as well as the characteristic dissipation ε0, should vary in time, depending on the tidal currents and stratification in the BBL. The eddy diffusivity KN = 0.2ε/N 2 showed an inverse dependence on the Richardson number Ri according to KN = K 0/ (1 + Ri/Rc ), where Rc is a constant and the diffusivity in nonstratified flow near the seafloor K 0 = u * κζ is specified using u * = u * ml .
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This paper presents a review of theoretical, experimental, and numerical studies of geometric attractors of internal and/or inertial waves in a stratified and/or rotating fluid. The dispersion relation for such waves defines the relationship between the frequency and direction of their propagation, but does not contain a length scale. A consequence of the dispersion relation is energy focusing due to wave reflection from sloping walls. In a limited volume of fluid, focusing leads to the concentration of wave energy near closed geometrical configurations called wave attractors. The evolution of the concept of wave attractors from ray-theory predictions to observations of wave turbulence in physical and numerical experiments is described.
Article
We study the propagation in three dimensions of internal waves using ray tracing methods and traditional dynamical systems theory. The wave propagation on a cone that generalizes the Saint Andrew’s cross justifies the introduction of an angle of propagation that allows to describe the position of the wave ray in the horizontal plane. Considering the evolution of this reflection angle for waves that repeatedly reflect off an inclined slope, a new trapping mechanism emerges that displays the tendency to align this angle with the upslope gradient. In the rather simple geometry of a translationally invariant canal, we show first that this configuration leads to trapezium-shaped attractors, very similar to what has been extensively studied in two-dimensions. However, we also establish a direct link between the trapping and the existence of two-dimensional attractors. In a second stage, considering a geometry that is not translationally invariant, closer to realistic configurations, we prove that although there are no two-dimensional attractors, one can find a structure in three-dimensional space with properties similar to internal wave attractors: a one-dimensional attracting manifold. Moreover, as this structure is unique, it should be easy to visualize in laboratory experiments since energy injected in the domain would eventually be confined to a very thin region in three-dimensional space, for which reason it is called a super-attractor.
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The head of the Laurentian Channel is a very dynamic region of exceptional biological richness. To evaluate the impact of freshwater discharge, tidal mixing, and biological activity on the pH of surface waters in this region, a suite of physical and chemical variables was measured throughout the water column over two tidal cycles. The relative contributions to the water column of the four source-water types that converge in this region were evaluated using an optimum multiparameter algorithm (OMP). Results of the OMP analysis were used to reconstruct the water column properties assuming conservative mixing, and the difference between the model properties and field measurements served to identify factors that control the pH of the surface waters. These surface waters are generally undersaturated with respect to aragonite, mostly due to the intrusion of waters from the Upper St. Lawrence Estuary and the Saguenay Fjord. The presence of a cold intermediate layer impedes the upwelling of the deeper, hypoxic, lower pH and aragonite-undersaturated waters of the Lower St. Lawrence Estuary to depths shallower than 50 m.
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An overview of physical oceanographic conditions in the Gulf of St. Lawrence in 2013 is presented as part of the Atlantic Zone Monitoring Program (AZMP). AZMP data as well as data from regional monitoring programs are analysed and presented in relation to long term means. St. Lawrence River annual mean runoff was near-normal but the spring freshet was above-normal. It began early, in March, consistent with early melt associated with the warmest March air temperatures since 1873, and persisted much longer than usual with peak runoff in May and an average runoff nearly as high in June. The seasonal maximal volume of sea ice was 6th lowest since 1969. A large portion of the winter mixed layer remained above-freezing by at least 0.6°C in early March, preventing further sea-ice formation. The August-September cold intermediate layer (CIL) had the third lowest volume (T < 1°C) since at least 1985. The CIL minimum temperature index for the Gulf in August-September was the third highest since 1985. The sea-surface temperature averaged from May to November over the Gulf was above-normal by +0.4°C. Deep water temperatures and salinities are increasing overall in the Gulf, with inward advection from Cabot Strait where temperature and salinity reached a record high (since 1915) in 2012 at 200 and 300 m, respectively. Temperature averaged over the Gulf at 300 m increased slightly in 2013 to reach the highest value since 1980. Temperatures at the depth of the temperature maximum (approx. 250 m) were above-normal in Esquiman Channel and central Gulf, exceeding 6°C, causing large areas of the sea floor to be covered by waters with temperatures > 6°C in these areas. Salinity at Cabot Strait at 300 m decreased to normal in 2013, accompanied by a decrease in temperature. While this could have signified an important change to cooler water masses entering the Gulf at depth, waters just as warm as the record of 2012 were observed again in Cabot Strait in March 2014, reaching 7.5°C. The 2013 near-normal conditions were therefore perhaps only a respite.
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A 1965 survey of currents and geostrophic currents in the St. Lawrence estuary is described. An innovation employed in the survey was to moor the strings of oceanographic bottles in the cross-section and trip them simultaneously. A tidal oscillation was detected in the vertical shear of the geostrophic current as well as in the vertical shear of the axial and cross-channel current components. The observations qualitatively confirm predictions from a simple theory that is presented for geostrophic response on one-and two-layer canals. The theory suggests that the period of resonant cross-channel oscillation is an important time scale since current fluctuations of much longer periods reflect accurately in the geostrophic current, while fluctuations of shorter periods may appear as considerable distortions in the geostrophic current. From this, it is concluded that a single determination of geostrophic current may represent neither the instantaneous nor the long-term average current. The average geostrophic current over a time interval longer than the resonant period may, however, represent the average current over the same interval. DOI: 10.1111/j.2153-3490.1970.tb01936.x
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A comparison is made between series of high frequency internal waves observed in the St.Lawrence estuary from an aircraft and in a field program at a later date. Wave generation is associated with the propagation of a warm surface front during each ebb flow. The number of waves, as evidenced by surface slicks, is thought to vary as does the stability of the upper layer of the water column. (A)
Chapter
The St. Lawrence Estuary exhibits an estuarine character between Quebec City and the Saguenay Fjord (Upper estuary) and a maritime character between the Saguenay Fjord and the Gulf of St. Lawrence (Lower estuary). Topographically modified motions are mostly suprainertial in the former section and sub-inertial in the latter. The shallow Upper estuary is dominated by high-frequency motions such as internal waves and tides, which are generated by interaction of the tidal flow with sills, banks and especially the shoaling region at the head of the Laurentian Trough. The deeper Lower estuary exhibits a variety of strong low-frequency motions including topographic waves and unstable shear waves.
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This report summarises, in an engineering form, the main processes of cohesive sediment behaviour, namely, erosion, deposition and consolidation. The data presented are intended to show the practising engineer which parameters are important in each of the processes and to enable broad estimates of the rates of erosion, deposition and consolidation to be made based on a limited knowledge of the field conditions. Where possible the report has been structured to present first the knowledge and then the procedures for making a prediction of that quantity. The work was carried out as part of a strategic research programme on cohesive sediment transport processes undertaken for the Department of the Environment, Transport and the Regions. The behaviour of cohesive sediment is controlled by a complex array of physical, chemical and biological factors, which are understood to varying levels of completeness. The usual methodology of engineering investigations which require a knowledge of the properties of cohesive sediment has been to determine either in-situ or in the laboratory the behaviour of the cohesive sediment. Accordingly, the data obtained is site specific. The properties of cohesive sediment will vary spatially within a site and to a greater extent will vary between sites. At present, it is not possible to predict the behaviour of a cohesive sediment from its physical and chemical properties alone but advances have been made in the applicability of the largely semi-empirical predictions used by adopting appropriate theoretical approaches to underpin the procedures, or by including a wider range of data in their calibrations.
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Near-surface current measurements from locations along the channel of the St. Lawrence Estuary between Trois Pistoles and Baie Comeau are examined for consistent evidence of internal tides. The harmonic constituents of the local tidal streams at each site were estimated by harmonic analysis of the records, and from these were subtracted estimates of the harmonic constituents of the local barotropic tidal streams (those due to surface tides alone). The residues are taken as estimates of the harmonic constituents of the local baroclinic tidal streams (those due to internal tides alone). The results indicate the presence of a progressive internal semidiurnal tide of the Poincare type and diurnal tide of the Kelvin type propagating seaward from the inland end of the Laurentian Channel. The character of the observed internal tide agrees well with that predicted by theory for the given stratificaion and topography. Possible practical significance of the internal tides in assisting mixing, crating ice pressure, and causing seasonal changes in tidal streams is discussed.
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A 10,000-km(2) hypoxic 'dead zone' forms, during most years, in the central basin of Lake Erie. To investigate the processes driving the hypoxia, we conducted a 2-yr field campaign where the mixing in the lake interior during the stratification period was examined using current meters and temperature-loggers data, as well as. 600 temperature microstructure profiles, from which turbulent mixing was computed. Near-inertial Poincare waves drive shear instability, generating similar to 1-m amplitude and 10-m wavelength high-frequency internal waves with similar to 1-m density overturns that lead to an increase in turbulent dissipation by one order of magnitude. The instabilities are associated with enhanced vertical shear at the crests and troughs of the Poincare waves and may be correlated with the local gradient Richardson number. Poincare wave-induced mixing should be an important factor when the Burger number < 0.25. The strong diapycnal mixing induced by the Poincare wave activity will also significantly modify the energy-flux paths. For example, we estimate that, in Lake Erie, 0.85% of the wind energy is transferred to the lake interior (below the surface layer); of this, 40% is dissipated in the interior metalimnion and 60% is dissipated at the bottom boundary. In smaller lakes, 0.42% of wind energy is transferred to the deeper water, with 90% dissipated in the boundary and 10% in the interior metalimnion.