Dynamics of slow suspension flows on the Black Sea abyssal plain

Abstract

This paper aims to develop a theoretical hydromechanical model designed to explain slow motion of thin sediment suspension layer over the Black Sea abyssal plain. The suspension flows are regarded as a new lateral deep sea sediment transport mechanism differing from turbidity currents and other gravity flows in minor mass scale and velocity. The suspension can flow as a heavy liquid denser than the surrounding clear sea water if its upper surface has an inclination to the horizontal plane. Estimated kinematic viscosity coefficient of the suspension is about 3·10⁻⁴ m²/sec. Laboratory measurements showed that the suspension has properties of a viscous incompressible fluid. Its motion can be described by the Navier-Stokes equations if the suspension density is less than 1.32 g/cm³. According to box corer and multicorer sampling, a suspension layer, up to 20 cm thick, exists above the sediment surface on the Eastern Black Sea abyssal plain. It can move over the abyssal plain as a near-bottom gravity driven suspension current, several tens of centimeters thick or less, with velocities from several meters up to several kilometers per day, depositing a millimeter-scale terrigenous mud lamina on the way. Our study was focused on the Eastern Black Sea basin where the flat slightly inclined abyssal plain provides favorable conditions for suspension flows motion and lateral deposition of laminated sequences from these flows out of turbidite sequences which dominate in the. Western basin with the Danube turbidite system. Rather weak near-bottom suspension flows are generated here on the shelf from rather small Caucasian rivers discharge plumes and move downslope to the abyssal plane through numerous submarine canyons.

Full text

Dynamics of slow suspension flows on the Black Sea abyssal plain
N.V. Esin
a
,
*
, I.O. Murdmaa
b
, N.I. Esin
a
, Y.D. Evsyukov
a
a
Southern Branch of the P.P. Shirshov Institute of Oceanology, Russian Academy of Science, 1-g Prostornaya Str., Gelendzhik, 353467, Krasnodar region,
Russian Federation
b
Shirshov Institute of Oceanology, Russian Academy of Science, 36 Nakhimovsky Prosp., Moscow, 117997, Russian Federation
article info
Article history:
Received 10 March 2016
Received in revised form
25 June 2017
Accepted 21 July 2017
Available online 1 August 2017
Keywords:
Mathematical modeling
Experiments
Navier-stokes equations
Viscous dense liquid
Lateral sedimentation
Cascading
Lamination
abstract
This paper aims to develop a theoretical hydromechanical model designed to explain slow motion of thin
sediment suspension layer over the Black Sea abyssal plain. The suspension flows are regarded as a new
lateral deep sea sediment transport mechanism differing from turbidity currents and other gravity flows
in minor mass scale and velocity. The suspension can flow as a heavy liquid denser than the surrounding
clear sea water if its upper surface has an inclination to the horizontal plane. Estimated kinematic vis-
cosity coefficient of the suspension is about 3$10
4
m
2
/sec. Laboratory measurements showed that the
suspension has properties of a viscous incompressible fluid. Its motion can be described by the Navier-
Stokes equations if the suspension density is less than 1.32 g/cm
3
. According to box corer and multicorer
sampling, a suspension layer, up to 20 cm thick, exists above the sediment surface on the Eastern Black
Sea abyssal plain. It can move over the abyssal plain as a near-bottom gravity driven suspension current,
several tens of centimeters thick or less, with velocities from several meters up to several kilometers per
day, depositing a millimeter-scale terrigenous mud lamina on the way. Our study was focused on the
Eastern Black Sea basin where the flat slightly inclined abyssal plain provides favorable conditions for
suspension flows motion and lateral deposition of laminated sequences from these flows out of turbidite
sequences which dominate in the. Western basin with the Danube turbidite system. Rather weak near-
bottom suspension flows are generated here on the shelf from rather small Caucasian rivers discharge
plumes and move downslope to the abyssal plane through numerous submarine canyons.
©2017 Elsevier Ltd and INQUA. All rights reserved.
1. Introduction
A new lateral sediment transport mechanism in the Black Sea
basin is described here in terms of hydromechanics, based on data
obtained during the multidisciplinary research carried out within
the International IAEA RER/2/003 Project (2004) where the first
author participated (Esin, 2003). The primary materials including
deep sea sediment samples for measurements and experiments
have been collected from the eastern abyssal plain of the Black Sea
and are later supplemented by new data from the Caucasus shelf
and continental slope (e.g. Esin, 2003; Khvoroshch et al., 2012;
Yakubenko, 2011; Zavialov et al., 2014).
Two abyssal plains of the deep Black Sea basin, eastern and
western, representing shallower analogues of oceanic abyssal
plains, differ considerably in their morphology and modern
sedimentation processes. The eastern plain mainly considered in
this paper represents a flat almost horizontal surface with the
maximum depth of the sea in its western part, covered with soft
fine-grained sediments overlain by a stable thin suspension layer.
We hypothesize that this suspension mainly derived from river
discharge, is responsible for deposition of varve-like laminated
sequences widespread among the recent sediments (Degens et al.,
1978; Oaie et al., 2003-2004).
Sedimentation in the Western deep basin complicated by the
huge Danube fan and other sedimentary features, is studied in
detail by Lericolais et al. (2013), Constantinescu et al. (2015) and
many other authors. We believe that slow suspension flows
described by our theoretical model also contribute to the laminated
sedimentary structure formation here, but are masked by other
processes of lateral sedimentation.
*Corresponding author.
E-mail addresses: ovos_oos@mail.ru (N.V. Esin), murdmaa@mail.ru
(I.O. Murdmaa), esinnik@rambler.ru (N.I. Esin).
Contents lists available at ScienceDirect
Quaternary International
journal homepage: www.elsevier.com/locate/quaint
http://dx.doi.org/10.1016/j.quaint.2017.07.025
1040-6182/©2017 Elsevier Ltd and INQUA. All rights reserved.
Quaternary International 465 (2018) 54e62

2. Geomorphological, hydrological, and sedimentological
setting
The deep Black Sea basin is subdivided into Eastern and Western
basins by the system of low topographic highs, called Hills and
Ridge in Russian literature. The Eastern Basin floor with maximum
depth of 2200 m represents an abyssal plain, a shallower analogue
of more than 3000 m deep oceanic abyssal plains. Bottom topog-
raphy of the Western Basin is complicated by the huge Danube fan
and other sedimentary or tectonic features, but a flat abyssal plain
also occurs around its depocenter.
Recent sedimentation on the western abyssal plain does not
principally differ from that on the eastern plain. On both plains,
varve-laminated organic rich coccolith ooze is described from the
uppermost hemipelagic unit. However, that from the Western Basin
is thought to be directly related to turbidite systems, whereas
laminated successions from the Eastern Basin likely deposited
independently (Constantinescu et al., 2015; Lericolais et al., 2013;
Oaie et al., 2003-2004). Very fine-grained surface sediments from
the eastern abyssal plain suggest still-water bottom conditions
which is on line with direct measurements. Absence of macro-
benthos owing to anoxic (euxinic) environment prevents from
bioturbation of sediments hence promoting preservation of the
laminated sedimentary structure.
The abyssal plain is approximately constrained by the contour of
2000 m (Fig. 1). Inclination of the eastern Black Sea abyssal plain
surface decreases from 5$10
2
at the periphery of the basin to
3$10
4
at its center (Goncharov et al., 1972). Generalised bathy-
metric profiles off the Caucasian and Crimean coasts (Fig. 2)
demonstrate gradual transition from the abyssal plain to the
continental slope without any continental rise, hence indicating
restricted sediment accumulation by turbidity currents at the slope
base aside of canyon fans. The concave shape of profiles supports
this suggestion.
Numerous submarine canyons cut the Caucasian continental
slope (Fig. 3) serving as pathways for any gravity driven sediment
transport from the shelf, including the suspension flows considered
in this study. The seismic profile along the canyon bed (Fig. 4) show
eroded bottom from steep slope and slump bodies from gentler
steps (Khvoroshch et al., 2012).
The continental slope is bathed by the hydrogen sulphide
polluted, higher salinity deep water almost up to the shelf brake.
This results in black color of recent sediments owing to staining by
authigenic iron sulphide (hydrotroilite) even if their organic carbon
(TOC) content does not exceed 1.5e2%, i.e. much lower than that in
sapropelic mud. We recovered a coretop layer, up to 75 cm thick, of
such black semi-liquid mud (with the water content of 280% and
wet density as low as 1.2 g/cm
3
) from the thalveg of a canyon.
(Moskalenko et al., 2006). These semi liquid sediments are appar-
ently unstable and may easily flow down-slope as a suspension
flow.
Small rivers discharge their particulate material load to the NE
Black Sea shelf forming suspension plumes adjacent to their
mouths well discriminated in satellite images (Fig. 5). Instrumen-
tally measured concentration of fine-grained particulate material in
these plumes reaches 60 g per liter and they extend up to a distance
of several kilometers from the river mouths (Zavialov et al., 2014).
Sinking to the bottom, the suspension behaves as a heavy liquid.
Being gravity forced, it moves toward the shelf edge and further
down-slope in canyons, with increasing velocity (up to 5 m/s) as a
suspension flow.
Fig. 1. Bathymetric map of the Black Sea with location of box corer sampling sites 4 and 11(asterisks) for the RER/2/003 Project (Marine Environmental Assessment of the Black Sea)
and profiles shown in Fig. 2.
N.V. Esin et al. / Quaternary International 465 (2018) 54e62 55

3. Material and methods
Inclination of the Black Sea abyssal plain surface decreases from
5$10
2
at the periphery of the basin to 3$10
4
at its center
(Goncharov et al., 1972). The bedding mode of the sedimentary
strata beneath the abyssal plain resembles the surface of a liquid
flowing from a permanent source over a slightly inclined flat
bottom.
Fig. 2. Generalised bathymetric profiles off Crimean and Caucasian coasts showing narrow shelves and concave slope profiles indicating absence of continental rises or fans. For
location see Fig. 1.
Fig. 3. Bathymetric map of a section of the NE Black Sea continental slope showing a series of submarine canyons. 1 - landslide formations; 2 - contours in meters; 3 - seismic
profiles. Modified from Khvoroshch et al., 2012.
N.V. Esin et al. / Quaternary International 465 (2018) 54e6256

As shown by our previous publications and experiments (Esin
and Shlesinger, 1986; Esin et al., 1989, 1991; Esin, 2003) the
suspension consisting of particular terrigenous material suspended
in sea water can be considered as a viscous incompressible fluid
movement of which is described by the NaviereStokes equations.
Relationship between the kinematic viscosity coefficient and den-
sity was experimentally established for the suspensions prepared
of natural deep-sea sediments from the Black Sea (Esin, 2003).
Fig. 6 shows that the kinematic viscosity coefficient rises slowly
with the increasing suspension density up to 1.25 g/cm
3
, being
approximately equal to the sea water viscosity in a laminar flow.
Further density increase results in a sharp viscosity rise that char-
acterizes the transition from viscous liquid to viscous plastic sedi-
ment which is able to flow if the shear stress
t
¼
Dr
gh sin
a
is more
than the critical shear stress
t
st
(
a
ethe angle of slope;
Dr
¼
r
s

r
,
r
s
esuspension density,
r
esea-water density).
Fig. 4. Seismoacoustic profile along the bed of Arkhip Canyon from the shelf break to the slope foot. Arrows show slump bodies on the eroded bedrock surface. Modified from
Khvoroshch et al., 2012.
Fig. 5. Example of a satellite image for the suspended matter concentration in the
surface layer of Mzymta and Psou rivers plumes. Modified from Zavialov et al., 2014.
Fig. 6. Relationship between the kinematic viscosity coefficient and density for the
suspensions prepared of natural deep-sea sediments from depth 1300e2000 m.
N.V. Esin et al. / Quaternary International 465 (2018) 54e62 57

As it is shown in (Lobkovsky and Garagash, 2002), earthquakes
may result in either a temporal fluidization of sediments, i.e.
transition from the viscous plastic consistence to the viscous liquid,
or a weakening of the sediment strength i.e.
t
st
that promotes
slumping. Both may produce additional portions of suspension on
the continental slope. Thus, effects of earthquake impacts may be
considered as a supplementary suspension source to the abyssal
plain.
Reaching the continental slope base, the suspension moves over
the very gently sloping abyssal plain towards the hypocenter of the
basin (~2200 m), located about 200 km from the Caucasus slope
base. According to our experiments, the suspension flows as a
viscous liquid, when its density ranges from 1.1 to 1.32 g/cm
3
. If the
density is higher, the suspension behaves as a viscous plastic body,
i.e. sediment (mud). Investigation of the water-bottom interface by
box corer sampling during the international project IAEA RER/2/
003 «Marine Environmental Assessment of the Black Sea Region»
(2004) showed that the sediment surface on the Black Sea abys-
sal plain is covered by a suspension layer which behaves as a
viscous liquid moving towards the basin center being driven by the
gravity forcing. Employees of the Institute of Oceanology took part
in the research on the IAEA project RER/2/003. After lifting the box
corers, the sediment was cut into layers of 1 cm thick. The layer of
the suspension, which was above the seabed, was separated in the
same way. This layer was recorded in almost all samples.
In this paper, we use instrumental determinations of the kine-
matic viscosity coefficient of the suspension (Esin, 2003). Possible
suspension flow velocities are calculated applying NaviereStokes
equations and experimentally determined kinematic viscosity co-
efficient values.
4. Some physical properties of the suspension
According to our experimental data (Esin, 2003), the suspension
flows over the modeled “sea bottom”like a “river”, as a more
viscous and dense liquid compared to sea water, even if the con-
centration of particular material is very low. Solid particles together
with surrounding water are forming an indivisible continuous
liquid that also possesses features of a discrete medium. The
discreteness is expressed by settling of solid particles onto the
bottom depositing a sediment layer during the suspension move-
ment. Settling velocity of the Black Sea deep-water sediment par-
ticles (excluding the finest fraction) in the immobile water is about
10.8 cm per hour.
Suspension flows on the shelf and continental slope of the Black
Sea are described in (Yakubenko, 2011). Maximum flow velocity
measured on the shelf, 3 m above the bottom, was as high as 0.5 m/
sec. The flow was directed seaward down across the shelf and
continental slope. The instruments fixed repeated approaches of
the flow front, its downward movement and termination. Sus-
pension flows are generated during river floods and strong storms
which resuspend sediments on the outer shelf. They represent
streams of opaque turbid bottom water moving downward under
gravity forcing. We have observed a semi-liquid black organic-rich
mud layer, up to 60 cm thick, with an extremely low shear strength
at a canyon channel of the Caucasus continental slope (Moskalenko
et al., 2006). It was likely deposited from the suspension flowing
down-slope from the shelf on its way towards the abyssal plane.
The suspension flows described here are playing a positive role
in the ecology of the Black Sea, because they transfer polluted
products of river discharge to the abyssal plain thus cleaning the
shelf. It seems that only this near-bottom transport mechanism
allows pollutants to cross the Black Sea Rim current and to disperse
those over the abyssal plain (Esin et al., 2011).
Vertical distribution of the suspension density on the abyssal
plain of the Black Sea was studied during the IAEA RER/2/003
project. Fig. 7 shows the vertical distribution of solid (particular)
phase weight in the suspension (g/cm
3
). Recalculating these values
to the suspension density we estimated that suspension containing
0.5 g/cm
3
of the solid phase has the density of 1.22 g/cm
3
and that
with 0.6 g/cm
3
of soli phase has the density of 1.27 g/cm
3
. The latter
value approximately corresponds to the density of transition from
the viscous liquid to the viscous plastic (mud) consistence. The
viscous plastic mud with the density above the transition value
does not further move, as the slope of abyssal plane is much less
than that necessary for gravity mudflow forcing. This should lead to
a progressive thinning of the suspension flow with increasing dis-
tance from the abyssal plain margin.
As shown in Fig. 7, box corer sampling confirmed that at least
8 cm thick suspension layer exists over the bottom surface at water
depths of 1900e2100 m. Its upper part contains 0.06 g per 1 cm
3
of
the solid phase that corresponds to the suspension density of
1.025 g/cm
3
. The lower part of the suspension layer contains
0.25e0.33 g/cm
3
of particular material having the density of about
1.15 g/cm
3
, thus lower than the value of transition to the viscous
plastic consistence. Therefore, at least 8 cm thick bottom layer of
suspension exists on the abyssal plain of the Black Sea which can
slowly move towards the depocenter of the sea. Kinematic viscosity
coefficient
n
of the suspension is about 3·10
4
m
2
/sec (Esin, 2003).
5. Gravity flow of suspension
A slow, steady flow of suspension on a horizontal or slightly
inclined plane can be considered as a steady flow of viscous
incompressible fluid. The flow is described using the Navier-Stokes
equations (Slezkin, 1955). In the case of the flat task, neglecting the
vertical velocity Vcompared to horizontal velocity U,aswellas
neglecting non-linear (inertia) members compared to the terms
describing the effect of viscosity, we obtain:
g
Dr
r
s
sin
a
1
r
s
vp
vxþ
n
v
2
u
vz
2
¼0;(1)
g
Dr
r
s
cos
a
1
r
s
vp
vx¼0:(2)
where Хaxis coincides with the sea bottom and is directed towards
the movement of suspension, Zaxis pointing upwards,
a
ethe
angle of bottom slope to the plane of the horizon, gethe accel-
eration of gravity, uethe velocity of suspension along the Х- axis,
r
ethe density of water,
r
s
ethe density of suspension,
Dr
¼
r
s

r
,p
ethe pressure in the suspension layer without the hydrostatic
pressure of water. Suppose we know the discharge of suspension
flowing over the bottom of the sea:
Z
h
0
udz ¼Q;(3)
where hethe thickness of the suspension layer.
The sticking boundary condition is used on the bottom: z¼0,
u¼0. Boundary conditions for the “free”surface of the suspension
flow: if z¼hthen p¼0,
n
vu
vz
¼
t
(
t
ethe shear stress on the upper
boundary). In first approximation we use
t
¼0. In reality, the flow
of water (situated above the suspension layer) enhances (
t
>0) or
slows (
t
<0) the movement of suspension flow. In a first approxi-
mation, considering the geological process it can be ignored. Also,
we assume that we know the value of hat the end of the viewed
section of the suspension flow: x¼x
0
,h¼h
0
. In these boundary
N.V. Esin et al. / Quaternary International 465 (2018) 54e6258

conditions the system of equations (1)e(3) is integrated following:
P¼
Dr
gðhzÞcos
a
;(4)
u¼g
Dr
2
nr
s
cos
a
tg
a
dh
dxh
2
;(5)
tg
a
dh
dx ¼3Q
nr
s
Dr
gh
3
cos
a
;(6)
dh
dx <0:
The highest velocity of flow at the surface of the suspension
flow, where z¼h:
u
max
¼g
Dr
2
nr
s
cos
a
tg
a
dh
dxh
2
:(7)
6. Suspension flow along the horizontal bottom
Suspension can move over the horizontal bottom (
a
¼0) if it
accumulates (i.e. if there is a permanent source of suspension) on
the horizontal surface so that the “free”upper surface of the sus-
pension has a slope relative to the horizon. Then, a pressure
gradient appears being oriented towards the movement direction.
Hence, the suspension itself creates the force which drives it along
the sea bottom. Fine-grained terrigenous material is delivered into
the deep basin from the shelf partially as turbid water “clouds”
within the water column over the continental slope, but mainly as
gravity driven suspension flows which descend via canyons down
to the slope base. We do not consider here episodic catastrophic
turbidity currents (instantaneous in the geological time scale)
which deposit turbidites, as well as other gravity mass flows.
Instead, we discuss relatively slow but rather permanent flows of
thin suspension layers which behave as a “heavy liquid”relative to
clear sea water. Such descending dense liquid (cold, saline or turbid
sea water) flows are known as cascading (e.g. Shapiro et al., 2003).
The suspension flows from the base of the continental slope to
the sea center over the nearly horizontal bottom. We calculate the
possible velocities of its movement and the thickness of the moving
layer. The solution of equation (6) (when
a
¼0) has the form:
h¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
h
4
0
þ12Q
nr
s
g
Dr
ðx
0
xÞ
4
s(8)
u¼3
2
Q2zh
4
0
þ
12 Q
nr
s
ðx
0
xÞ
g
Dr

1
=
4
z
2

h
4
0
þ
12 Q
nr
s
ðx
0
xÞ
g
Dr

3
=
4
(9)
We estimate the discharge of sedimentary material which is
supplied to the base of the continental slope. According to
Fig. 7. Vertical distribution of solid (particular) phase weight (weight concentration g/cm
3
) in the suspension (Project RER/2/003, 2003). a) estation BS-4, sea depth 2147 m; b) e
station BS-11, sea depth 1880 m.
N.V. Esin et al. / Quaternary International 465 (2018) 54e62 59

Khachanuridze (1990), rivers carry annually about 10
7
m
3
terrig-
enous material from the Caucasian coast of the Black Sea. The
coarse material with a particle size of more than 2 mm is deposited
in the coastal zone in the amount of 1:5$10
6
m
3
, and the fine
fraction (8:5·10
6
m
3
) forms the shelf deposit, continental slope
deposit and deep basin deposit of the Black Sea. Calculations of the
movement of the suspension are made from literature sources.
Given the length of the continental slope base, the average annual
discharge of the terrigenous material at the base of the continental
slope is 10
6
m
3
=ðm$secÞ(i.e. the discharge of solid phase per unit
of the continental slope base length).
The particular material discharge to the suspension flow from
the canyons of large Georgian rivers is even more abundant. If we
take runoff of suspended sediment amount of 3650000 m
3
=year
for the Chorokha River (Khachanuridze, 1990), and the width of the
suspension flow 1000 m, then we get the following average annual
discharge of sedimentary material: 1:2$10
4
m
3
=ðm$secÞ.
The greatest discharge of suspension flow is observed during the
freshet, as a rule it is going for less than one month. At this time, the
discharge of solid phase of the suspension flow can be tentatively
10
3
m
3
=ðm$secÞ. In order to transit this sedimentary material as
the suspension with the density of 1:1tn=m
3
, the discharge of
suspension flow should be equal: Q¼8$10
3
m
3
=ðm$secÞ.
Equations (8) and (9) make it possible to estimate parameters of
the suspension flow process in different situations: for different
values of the viscosity, density and discharge. Equations (5), (6), (8)
and (9) are suitable for the study of the bottom suspension flow
from the coast to the sea center.
Assume that the distance (x
0
), which is moved by the suspen-
sion flow on the horizontal bottom (described by equations (8) and
(9)), equals 10
5
m. According to the results of IAEA project RER/2/
003 (2004), the estimated thickness of suspension layer was about
9cm(h
0
¼0:09 m) at the end of the flow, although it is actually
thicker. The calculations were performed for the following pa-
rameters:
n
¼2$10
4
m
2
=sec;
r
s
¼1100 kg=m
3
;
Dr
¼100 kg=m
3
;Q¼10
6
and 8$10
3
m
3
=ðm$secÞ. The calcula-
tion results are shown in Table 1.where 
dh
dx

av
ethe average slope
of the “free”surface of the suspension flow.
For the calculations we assumed that all the sedimentary ma-
terial (which is come to the base of the continental slope) is
transferred to the sea center by the suspension flow along the
horizontal bottom. The thickness of the suspension flow is tens of
centimeters at the margin of the abyssal plain and centimeters in
the sea center.
Thus, the huge amounts of terrigenous material (which are
brought by rivers to the shelf) are transported into the deep basin
by the gravity suspension flow centimeters or tens of centimeters
thick.
7. Suspension flow over the inclined bottom
According to (Goncharov et al., 1972), the minimum inclination
of bottom in the center of the Black Sea is 3$10
4
(3 m per 10 km).
The steepest slope of the “free”upper surface of suspension layer
(which initiates the flow over the horizontal bottom) is about
8·10
6
. It follows that in the study of current movements of sus-
pension on the Black Sea abyssal plain, the value of
dh
dx
can be
neglected compared to tg
a
. After completing this simplification in
the expressions (5) and (6), we obtain the formula for calculating
parameters of a plane-parallel flow of suspension on the inclined
bottom:
U¼g
Dr
2
nr
s
2zh z
2
sin
a
;(10)
h
3
¼3Q
nr
s
g
Dr
sin
a
:(11)
The flow velocity at the upper flow surface is:
U
max
¼g
Dr
h
2
2
nr
s
sin
a
:(12)
The average velocity of the suspension flow is determined by the
formula:
U
av
¼g
Dr
h
2
3
nr
s
sin
a
:(13)
Calculations of suspension flow parameters are performed for
the same values
r
s
,
Dr
,
n
and Qand for the three possible bottom
slopes: sin
a
1
¼3·10
4
(abyssal plain), sin
a
2
¼3·10
3
(shelf),
sin
a
3
¼3$10
2
(continental slope). The results are shown in
Table 2.
Table 2 shows that the average suspension flow velocity varies
widely efrom meters to kilometers per day, depending on the
discharge of suspension flow and slope of the bottom.
8. Possible sedimentological and palaeoceanographic
implications
The slow suspension flows considered here can explain the
deposition mechanism of laminated (varved) sediments wide-
spread among the Quaternary deposits of the Black Sea abyssal
plain (e.g. Ross et al., 1978; Degens et al., 1978). Distinct thin
(millimeter-scale) lamination with rhythmic regular succession of
dark (terrigenous sapropelic mud) and light (nannofossil ooze)
duplets resembling annual varves comprises a considerable portion
of the Upper Quaternary section in both Eastern and Western ba-
sins. The laminated intervals are mainly pertained to deposits of
warm climatic periods such as the Karangatian (Eemian) and Neo-
Chernomorian (late Holocene to Recent). Submerged shelf during
these periods of high sea level stand provided conditions for
development of the cascading mechanism. Turbidites mainly occur
within the glacial (low sea level stand) sections (Ross et al., 1978)
when shelf emerged and rivers discharged directly to the conti-
nental slope.
Table 1
Calculation results of the suspension flow over the horizontal sea bottom.
NQ,m
3
m
1
sec
1
h,m(х¼0) 
dh
dx

av
u
av
,m=day
х¼0х¼10
5
110
6
0.14 4$10
7
0.6 0.8
28$10
3
0.7 6$10
6
144 864
Table 2
Parameters of the suspension flow over the inclined sea bottom.
NQ,m
3
m
1
sec
1
sin
a
h;mU
av
,m=day
110
6
3$10
4
0.013 6.9
3$10
3
0.006 14.6
3$10
2
0.003 29.2
210
3
3$10
4
0.13 665
3$10
3
0.06 1440
3$10
2
0.03 2880
N.V. Esin et al. / Quaternary International 465 (2018) 54e6260

The mud laminae of varves are likely deposited from the slow
suspension flows described in this paper. As it is shown above, the
bottom water suspension is formed over the shelf during river
floods discharge and strong storms, moves down-slope (mainly
through submarine canyons) as a gravity driven dense liquid by the
cascading mechanism (Shapiro et al., 2003). Reaching the slope
base, the suspension from different canyons is united into a com-
mon planar flow that further moves slowly towards the depocenter
of the abyssal plain depositing a thin terrigenous mud lamina on
the way. The suspension flow is thinning seaward from several
meters in canyons to centimeter-scale in the center of the abyssal
plane. Thickness of individual laminae in the laminated successions
decreases correspondingly to millimeter or even submillimeter
scale in the area most remote from the continental slope.
The light nannofossil-rich laminae of varves are deposited dur-
ing seasons of a less abundant terrigenous material supply between
the river floods when the vertical nannofossil flux from the surface
water dominates over mud accumulation. However, sharp bound-
aries between the light and dark laminae suggest that terrigenous
suspension flows characterized by much higher seimentation rates
control the formation of laminated sedimentary structure, rather
than phytoplankton blooms.
The lamination generated by suspension flows was well pre-
served during warm periods of the Black Sea connection with the
World Ocean when saline Mediterranean Sea water inflow led to
the deep water anoxia, as today. The lamination was likely
disturbed owing to bioturbation, when the basin was totally or
partially isolated from the World Ocean and represented a lacus-
trine basin filled with the well ventilated semi-fresh water (as at
the Neoeuxinian stage). Therefore, the lack of lamination in
dominating terrigenous mud intervals recovered at Site 379 (Ross
et al., 1978) does not necessarily mean that the slow suspension
flows have not contributed to their deposition and thus, to the
sedimentary filling of the Black Sea basin as a whole, besides
turbidites.
9. Discussion and conclusions
The simplified theoretical model for slow gravity driven sus-
pension flows over the almost horizontal flat eastern Black Sea
abyssal plain undoubtedly needs further hydrophysical and sedi-
mentological testing. Nevertheless, lack of internal contradictions
in the mathematical processing provides an outlook for its further
improvement in order to understand generation of the suspension,
its behavior on the shelf, fast down-slope movement in submarine
canyons, slow spreading over the abyssal plain, and final settling of
suspended material to grow up the deep sea sediment strata.
We believe that slow gravity driven suspension flows represent
an effective new lateral sediment transport mode different from
both well known turbidity currents and contour currents which
deposit turbidites and contourites respectively. Unlike instanta-
neous noncontiguous turbidity currents happening with a century
scale frequency, the suspension flow movement is contiguous,
although may be pulsating. They do not need forcing by bottom
currents necessary for the contour currents, but move due to
gravity forcing realized either by bottom sloping or by inclination of
their upper surface, as shown in the model description above. A
suspension flow needs only constant sufficient feeding with new
portions of suspended particulate material to maintain inclination
of its upper (“free”) surface. Suspension flow moves under the ac-
tion of gravity in the conditions of either the inclined bottom, or the
inclined free surface of flow or both.
According to the hydromechanics theory, suspension moves as a
viscous liquid only if individual solid particles are so close to each
other that they may interact through attached water cover. In these
conditions, the water with suspended sediment particles behaves
in the sea as a liquid heavier than surrounding water. In the water
with lower concentration of solid particles, they do not interact.
The artificial suspension made of the deep-water Black Sea sedi-
ment for our experiments behaved in the sea as a viscous liquid
when its density is within the limits 1.01e1.3 g/cm3. A suspension
with higher density would turn into viscous plastic sediment. (Esin,
2003).
In the NE Black Sea, numerous small rivers discharge sediment
laden freshwater to the coastal area of the narrow shelf where
plumes are formed during spring or catastrophic rainfall floods
(Fig. 5). A distinct visible boundary always separates a turbid sur-
face water plume at river mouth from surrounding pure water. Well
expressed in satellite images (Fig. 5), this boundary is also
confirmed by instrumental measurements (Zavialov et al., 2014).
Near-bottom suspension flows are likely generated from the sur-
face layer suspended material on the outer shelf due to sinking of
solid particles into the previously existing suspension. This leads to
a sharp decrease in sinking rate of fine-grained material which stay
in suspension, whereas coarse fractions fall to the bottom. The
more concentrated near-bottom suspension layer with rather
distinct upper boundary flows toward the shelf edge along the
gently inclined shelf. Being caught by canyon heads it moves down-
slope with high velocity (up to 5 m/s) eroding canyon banks and
hence increasing own density that in turn, results in acceleration of
the flow.
Special experiments performed within the framework of the
international project RER/2/003 showed that a suspension layer, up
to 20e25 cm thick, able to flow as a viscous liquid overlies the
bottom surface throughout the abyssal plane. Movement of a sus-
pension flow is stimulated by the potential energy of its upper
layers. They exert pressure to lower layers and as a result, the
suspension moves seaward. The theory afirms that the flow velocity
may reach values of cm/s or even m/s on the abyssal plane at the
early phase of its movement (Yakubenko, 2011). Our calculations
above support these estimates.
Implication of the suspension flows described here to the recent
deep sea sedimentation is still poorly understood. We hypothesize
that the modeling of their activity on the eastern Black Sea abyssal
plain considered in this study helps to elucidate the problem of
fine-grained terrigenous material transport to the laminated se-
quences widespread among the recent (Holocene) deposits of the
plain and described by many authors (e.g. Degens and Ross, 1974;
Degens et al., 1978; Oaie et al., 2003-2004; Schimmelmann et al.,
2016 and references therein). However, the dark-colored organic-
rich (and stained by hydrotroilite) laminae constitute only a sub-
dued proportion in the millimeter-scale varve-type duplets of the
laminated coccolith ooze from the uppermost Lithozone 1 by Oaie
et al., (2003-2004). We assume that the dominant coccolith ooze
was deposited by vertical hemipelagic sedimentation on the way of
the near-bottom suspension layer movement over the abyssal plain
surface, but their sharp boundaries have been shaped by the next
mud lamina deposition.
The transition from laminar flow to turbulent flow occurs at a
critical Reynolds number R¼
ul
n
, where uethe velocity of the flow,
lethe thickness of the suspension layer,
n
ethe kinematic vis-
cosity coefficient. The value of the critical Reynolds number
R
cr
¼3$10
5
(Slezkin, 1955.).
We have established the values of u,l,
n
to calculate the Reynolds
number, which characterizes the flow of the suspension on the
abyssal plain of the Black Sea. To calculate R, we took the values that
give the maximum R. The value of
n
is 3·10
4
m
2
/s (Esin, 2003). The
figures in this article show that when the density increases to
1200e1400 kg/m
3
, the suspension turns into a viscous-plastic body.
N.V. Esin et al. / Quaternary International 465 (2018) 54e62 61

The density range of the suspension lying at depths of
180 0 e2000 m is below the indicated densities. Consequently, there
is a movable suspension. The calculated maximum flow velocity of
the suspension is 7680 m/day, or 0.09 m/s. In the experiments of
the project RER/2/003, only a part of the thickness of the moving
suspension is determined. According to the approximation, its
thickness is about 20e25 cm. Thus, we take l¼0,2 m. According to
our values of the parameters, we find R¼60. Thus, the number Rfor
the flow of the suspension flowing along the seabed is 4 orders of
magnitude smaller than R
cr
. Consequently, this value characterizes
a stable laminar flow. The physical explanation for this phenome-
non is that in the thin bottom layer of the suspension, the viscous
forces prevail over the forces of energy.
The velocity of the suspension flow, indicated in the article,
equal to 0.5 m/s is fixed in the zone of transition from the shelf to
the continental slope at depths of 80e100 m, where the bottom
slope sharply increases. In such areas, the thickness of the sus-
pension layer decreases and its velocity increases. This is shown by
the theory of the motion of water (Esin et al., 2010, 2014). On the
shelf, the suspension layer can reach many meters, and its flow
velocity reaches values m/s.
The suspension flow mechanism according to our model is
possibly also valid for explanation of various laminated sedimen-
tary structures revealed by comprehensive studies in the Danube
fan and adjacent western abyssal plain (e.g. Lericolais et al., 2013;
Constantinescu et al., 2015 and many others). Although contribu-
tion of the slow suspension flows to deposition of different lami-
nated sequences is masked here by more intensive turbidity
currents and other gravity flows activity, associated fine-grained
laminated sediments might well be deposited by suspension
flows similar to those described from the eastern abyssal plain.
More perfective mathematical modeling is necessary to solve
problems raised during elaboration of the simplified model pre-
sented in this paper.
Acknowledgements
This study is a contribution to the UNESCO International Geo-
science Programme (IGCP) Project 610. The work is partially sup-
ported by the Russian Foundation for Basic Research, Project 16-35-
00441 (NIE) and by the Russian Science Foundation, Project 14-50-
00095 (IM).
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