Modelling of Marina Forced Flushing
LALE BALAS1 and ASU ĐNAN2
1Department of Civil Engineering, Engineering Faculty
2 Department of Construction Education, Technical Education Faculty
Gazi University
06550Ankara TURKEY
1 lalebal@gazi.edu.tr, http://www.mmf.gazi.edu.tr/insaat/english/academicstaff/cv/lalebalasi.htm
2 asuinan@gazi.edu.tr, http://www.fbe.gazi.edu.tr/kazalar/English/asuinani.htm
Abstract: - Marinas located along the coastline of an enclosed sea are subjected to water quality problems due to
insufficient water exchange resulting from the weakness of the tidal motion. For such marinas forced flushing measures
may need to be designed. In this paper, a forced flushing scheme for enhancing flushing rates of marinas in enclosed seas
is discussed. As the forced flushing scheme inflow caused by a wave pump in the form of a surface current with a high
momentum is investigated. Experiments on the induced circulation patterns by the use of a wave pump were performed in
the laboratory and forced circulations were simulated by the developed three dimensional hydrodynamic and transport
model, HYDROTAM-3. Turbulence has been simulated by a two equation k-ω turbulence model. Model predictions
provided encouraging results. HYDROTAM-3 reproduces the velocity field that is in good agreement in the intensity
and spatial scale with the current measurement.
Key-Words: - Marina, forced flushing, modeling, turbulence, wave pump, mechanical pumping, finite element,
hydrodynamic, transport.
1 Introduction
The construction of a marina disturbs the natural balance
of the coastal system and normally deteriorates the water
quality in and around the project site. The breakwater,
purpose of which is to provide a physical barrier to waves,
can become a barrier to other natural processes as well.
Water enclosed in a marina basin has a restricted contact
with the outside sea and water exchange is possible only
through the entrance. The cross sectional area of the
entrance is usually small and the exchange is low
especially in areas where the tidal range is small [1]. The
presence of piers and crafts complicates the situation.
Water which enters into the basin can not circulate freely.
Limited water circulation may result in poor water quality
levels in the marina. The most decisive factor for water
quality in marinas is the flushing ability, that is, the level
of water exchange with outside. It has generally been
assumed that the most adverse biological effects within a
marina may be prevented, if flushing is sufficient and
upland drainage and other pollutants are diverted away
from the marina.
The tidal motion is the main agent causing the flushing of
marinas located on coastlines where the tidal range is
sufficiently large [2]. There are studies performed on the
optimum aspect ratio of a marina, i.e. the ratio of basin
length to basin width (L/B) [3]. When there is a strong
tidal forcing, one general result is that if the aspect ratio
is in between 1/3 and 3, the flushing quality is the best.
Dipole formation would also effect the tidal flushing
mechanism [4]. The tidal ranges along the shores of
Turkey which is surrounded by the enclosed seas are
typically in the order of 0.2 to 0.3 meters. Such a weak
tidal motion can not alone induce flushing action to
maintain the water inside the marina at a reasonable clean
state. In such situations, it is often necessary to apply
some special design features to enhance flushing of
marinas [5]. One such water quality improvement scheme
for relatively small marinas is to flush out water inside the
marina by a wave pump [6]. An alternative scheme is the
removal of the polluted marina water from time to time by
a forced outflow from an intake [7]. If the tidal forcing is
not strong or there exists a broad continental shelf,
meteorological forcing could be dominant. When the
density gradients are significant, density currents could
contribute to the flushing as well [8]. Flushing ability of
marinas located along shores of lakes, enclosed seas or
river inlet marinas usually is not sufficient due to very
small tidal ranges. In this study, the use of wave pump to
force a jet of clean water inside the marina to improve
flushing performance has been investigated. Both
physical and numerical models are used in the
determination of induced circulation patterns and the
results obtained are compared.
WATER AND GEOSCIENCE
ISSN: 1790-5095
78
ISBN: 978-960-474-160-1
2 Numerical Model HYROTAM-3
The developed implicit baroclinic three dimensional
hydrodynamic transport model (HYROTAM-3), is
capable of computing the water levels and water particle
velocity distributions in three principal directions by
solving the Navier-Stokes equations [9]. The numerical
model can simulate the flows induced by the density
currents. The density of sea water is a function of its salt
content (or salinity) and its temperature. The temperature
and salinity variations are calculated by solving the three
dimensional convection-diffusion equation. As the
turbulence model, modified k-ω turbulence model is
used. Model includes two equations for the turbulent
kinetic energy k and for the specific turbulent dissipation
rate or the turbulent frequency ω [10].
The turbulent kinetic energy equation is given by
[11];
kFP
z
k
zdt
dk
kk
ϖβνσ
** )( −++
∂
∂
∂
∂
=
(1)
and the specific dissipation rate equation is given by;
2*
)(
βϖ
ϖ
α
ϖ
νσ
ϖ
ϖϖ
−++
∂
∂
∂
∂
=FP
kzzdt
d (2)
where horizontal diffusion terms in which q is k or ω, are;
y
q
y
+
x
q
x
=
F
q
∂
∂
∂
∂
∂
∂
∂
∂
νσνσ
** (3)
The stress production of the tubulence is defined by;
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
∂
z
v
+
z
u
+
x
v
+
y
u
+
y
v
2+
x
u
2 = P
22
22
2
νν
(4)
Eddy viscosity is calculated as;
ϖ
ν
k
=
(5)
At high Reynolds Numbers, the constants are used as;
α=5/9, β=3/40, β*=9/100,σ=1/2 and σ*=1/2. Whereas at
lower Reynolds numbers they are calculated as;
6/R1
6/R40/1
T
T
*
+
+
=α
;1*
T
T)(
7.2/R1
7.2/R10/1
9
5−
α
+
+
=α ;
ϖν
k
R
T
=
;4
4
*
)8/(1
)8/(18/5
100
9
T
T
R
R
+
+
=
β
(6)
where, RT is the Reynolds number of the turbulence. The
solution method is to use a composite finite difference-
finite element method [9]. Equations are solved
numerically by approximating the horizontal gradient
terms using a staggered finite difference scheme.
3 Modelling of Forced Flushing in Datça
Marina
Model has been applied to Datça Marina to predict the
forced circulation patterns by the use of a wave pump.
Model predictions are compared with the measurements
performed in the Laboratory. Datça Marina is located 2
km south of the town of Datça and is protected by a
breakwater approximately 600 meters long (Fig.1a-b).
Laboratory experiments were carried on the forced
flushing of the marina with the wave pump. The length
scale of the marina was 1:100. The prototype length of
the basin is 460 m and the width is 220 m. The water
depth inside the marina changes from 1.6 m to 15.3 m in
the prototype. Governing forces concerned were gravity
and inertia forces whereas the effects of surface tension
and viscosity were negligible. Therefore, Froude Law
was the best to describe the phenomenon. According to
Froude Law, Froude numbers for both model and
prototype must be equal, therefore the velocity scale was
calculated as 1:10.
DATÇA
Scale : 1/1000000
28
o
AEGEAN SEA
TURKEY
(a)
0 100 m
-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
-20
-15
-10
-5
0
water depths (m)
(b)
Fig. 1. (a) Location of Datça Marina location, (b) Water
depths(m) and layout of Datça Marina
WATER AND GEOSCIENCE
ISSN: 1790-5095
79
ISBN: 978-960-474-160-1
The wave pump (Fig.2) is located on the main breakwater
and aligned with the dominant wave direction without
forming too much perturbation inside the marina. This
can be achieved by a proper arrangement of the pump.
Inflow caused by the pump should be surface current
with a high momentum rather than waves entering the
basin. The wave pump consists of two vertical walls
starting from a certain depth and getting closer to each
other as they reach the breakwater. The aim is to compact
the wave energy at a narrower section and thus to get
higher wave heights.
In the vicinity of the breakwater a ramp with a slope of
3:8 is placed at the bottom so the depth is reduced
artificially. With the increasing wave height and
reducing water depth, waves are forced to break on the
ramp and so only the flushing effect of waves is let in the
marina with a high velocity.
Fig.2. Details of a wave pump
Datça Marina is subjected mainly to waves from NNE,
NE, ENE, E, ESE, SE, SSE and S directions. The related
wave rose based on the hourly wind data of the period
1982-2006 is given in Fig.3 [12]. Waves propagating
from S become ineffective due to refraction and shoaling
as they reach the marina site. The topography of the
marina prevents the northern winds to be effective due to
very limited fetch distances although they might be
considered as the dominant wind directions. Among the
rest of the directions, SE is defined as the most
significant wave direction. Nevertheless, due to the
limited fetch distances, significant wave heights for all
directions are small being less than 1.5 m. Therefore SE
was decided as the direction of the wave pump. Therefore
SE was decided as the direction of the wave pump. The
test case for the significant wave period of 5 sec and the
significant wave height of 1.5 m is presented in this
paper.
Fig.3. Datça wave rose (directional frequencies and wave
heights) for the period of 1982-2006.
The paths followed by the floats in the physical model
(Fig.4a) were compared with the results obtained from
the numerical model (Fig.4b). The average velocities
along the paths followed by the floats in both physical
and numerical models are compared in Table (1).
Table 1. Comparison of the average velocities along the
paths followed by the floats in physical and numerical
models for the wave pump (Velocity scale = 1:10).
Wave Pump
Velocity (cm/s) Path no
Physical
Numerical
Error
(%)
1 1.92 1.86 3.1
2 2.13 2.40 12.7
3 3.72 3.85 3.5
4 3.47 3.55 2.3
5 5.85 5.58 4.6
6 6.21 6.32 1.8
7 0.52 4.22 -
WATER AND GEOSCIENCE
ISSN: 1790-5095
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ISBN: 978-960-474-160-1
(a)
(b)
Fig.4. : Wave pump location, a) paths followed by the
floats in the physical model, b) results obtained from
numerical model.
Physical and numerical model results show nearly the
same circulation patterns with almost the same average
velocity components. Except from the path no 7, model
again provides more or less the same results. Some floats
released at the mouth of the pump and catch the right
flow path reach considerably high velocities. They seem
to travel on almost straight paths and thus leave the basin
quickly. This causes average current velocities in the
range of 5 – 6.5 cm/s in prototype scale. For the float
released at the end of the pier (path no 7), in the physical
model there occurs a reverse gyre with a quite small
velocity, almost a dead region. However such a gyre
could not be simulated by the numerical model. Reason
for this could be the disability of the turbulence model
not to account for the probable reflection that might
occur at the end section of the pier. Applied turbulence
model reproduces the velocity field that is in good
agreement in the intensity and spatial scale with the
current measurement data.
It is obvious that water entering to the basin with a high
momentum will influence the water particles on the way
highly. Shear effect of flow propagating rather with a
high current speed again forms shear force nearby. Shear
effect causes water particles to move on closed orbits
especially on the upper left corner of the basin. Whereas,
a small and slow circulation may be observed at the right
section. In addition to this, basin may be said to be
flushed better under these circumstances. Despite the
closed and round circulation pattern at upper left corner,
the whole basin is almost totally flushed.
Wave pump alternative has an attraction with its being
free of cost of operation. Once the structure is
constructed properly, flushing mechanism is a result of
natural phenomenon related with the waves. There is not
any operation cost other than maintenance, which will be
taken into consideration in some years period. On the
other hand, the system causes extra perturbation due to
the intrusion of jet flow especially in the vicinity of the
pump. This will bring more agitation inside the marina
and needs more attention to manoeuvring and mooring
inside the marina. In addition to these, since the energy
utilized by the wave pump is the energy of the wind
waves present at the marina site, the degree of its
contribution to the flushing totally depends on the
existence of the waves. The pollution of the marina is
expected to be the severest during summer months. So,
small number of occurrence of waves during summer
months may cause wave pump not to be very effective
for flushing.
WATER AND GEOSCIENCE
ISSN: 1790-5095
81
ISBN: 978-960-474-160-1
4 Tidal Flushing
The dominant tidal constituent for the area is M2 tide.
Along the Turkish coastline, the tidal ranges are small,
typically in the order of 0.2 to 0.3 meters. The tidal flushing
ability of the marina is examined by a one dimensional
flushing model.
A nonconservative substance with a first order decay
reaction is considered . Its concentration is Co at the start
of the computations. The intrusion of the pollutant into the
coastal water body continues at a constant rate P. As the
model is one dimensional, the pollutant concentration is
assumed not to vary spatially. This requires complete
mixing inside the water body at all times. The model
equation, stating the conservation of the pollutant mass in
the enclosed water body is written as [5]:
V
P
C)
V
Q
k(
dt
dC ++−=
(7)
in which, C: the instantaneous pollutant concentration; k:
decay coefficient; Q: entering discharge; V: water volume
inside the marina.
When the flushing discharge is due to the tidal action,
the bulk conservation equation becomes:
)tideebb(T)
2
1
n(tnTfor
V
P
kC
dt
dC K+≤≤+−=
(8)
)tideflood(T)1n(tT)
2
1
n(for
V
P
C)
V
Q
k(
dt
dC K+≤≤+++−=
(9)
in which, T: tidal period; n: a positive integer (“zero”
included) and t=0,T,2T,…, are the times of mean high tide
level (i.e. the onset of the ebb tide). The timely variations
of the tidal discharge Q and the water volume V are used
as:
)wtsin(wRA
2
1
Qs
=−
(10)
)wtcos(RA
2
1
VV ss +=
(11)
where, As: Surface area at mean sea level; Vs: Mean tide
level volume; R: Tidal range (from mean low level to mean
high level) and w:2π/T.
The solution giving the pollutant transport concentration
at the time of high tide after the n th tidal cycle is:
a
n
o
n
nC
a
ab
CaC −
−
+=
1
)1(
(12)
in which,
kT
e
M
M
a−
+
−
=
1
1
(13)
+
++
+
−−−
+
=−)
)(
1()
)(
1()1(
1
2
22
2
2
22
2
2
wkM
k
ae
wkM
k
ae
M
M
kT
b
T
k
T
k
(14)
s
a
s
s
V
PT
C
R
h
RA
V
M2
;2
2===
(15)
where, h: mean water depth, M: flushing parameter. If the
substance is conservative then k=0 and equation for Cn still
holds if the parameters a and b are redefined as:
1
)
1
1
1(
;
1
1
+
+
−
+
=
+
−
=
M
M
M
M
b
M
M
a
(16)
The one dimensional model presented above is applied to
Datça Marina. The model provides a quick assessment of
the degree of tidal flushing to be expected. The mean depth
of the Marina is 5 m. and the surface area is about 101000
m2. The tidal motion at the site is semi-diurnal type. The
mean tidal range is about 0.2 m. The flushing parameter
has a value of 50. The Cn/Co ratios are computed for a
conservative pollutant and results are plotted in Fig. 5.
Fig. 5. The changes of pollutant concentration with time
for various rates of pollutant addition.
Fig.5 depicts the situation that if no pollutant is
introduced into the marina (i.e. for Ca/Co=0), it takes 116
days that require 219 tidal cycles for the pollutant amount
in the marina to be flushed out by the tidal currents alone
up to level of 99 % , i.e. to have the value of Cn/Co=1%.
If the pollutant continues entering the marina waters, the
flushing period of the marina gets much longer.
Furthermore, it is computed that Cn=Co for all times if
the pollutant addition rate is such that Ca/Co=0.01. As it
is also observed from Fig.5 the cleansing of the water
body can not be realized at all if Ca/Co>0.01. These
indicate that flushing of the marina by the tidal motion
alone is far from being sufficient for self cleansing. With
the application of the wave pump, the flushing ability of
the marina increases about 12 times respectively, as a
result of the increase in the exchanged volume of the
water body.
WATER AND GEOSCIENCE
ISSN: 1790-5095
82
ISBN: 978-960-474-160-1
4 Conclusions
Forced flushing of a marina is investigated by both
physical and numerical model studies. Need for forced
flushing of Datça Marina arises due to the limited tidal
flushing which is generally the case in Turkish marinas.
Flushing of marinas using special structures like a wave
pump can be said to be an effective way for forced
flushing of Datça Marina. It is for sure that utilization of
a wave pump in a Marina will result in a better water
quality.
The three dimensional hydrodynamic transport model
(HYDROTAM-3) presented in this paper is shown to be
capable of predicting forced circulation patterns and the
level of flushing enhancement with very reasonable
accuracy. The model which can serve as a powerful design
tool, may also be used to predict the natural flushing rates
caused by tidal motion, wind effect, a water inflow due to
longshore currents driven by breaking waves, and fresh
water inflow in the case of a river marina.
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WATER AND GEOSCIENCE
ISSN: 1790-5095
83
ISBN: 978-960-474-160-1
