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Journal Article•DOI•

1DV bottom boundary layer modeling under combined wave and current: turbulent separation and phase lag effects

Katell Guizien, C. Marjolein Dohmen-Janssen1, Giovanna Vittori2•
University of Twente1, University of Genoa2
01 Jan 2003-Journal of Geophysical Research (American Geophysical Union)-Vol. 108, pp 16-1-16-15
TL;DR: In this paper, a new k-ω turbulence model was proposed for 1DV oscillating bottom boundary layer in which a separation condition under a strong, adverse pressure gradient has been introduced and the diffusion and transition constants have been modified.
Abstract: On the basis of the Wilcox [1992] transitional k-ω turbulence model, we propose a new k-ω turbulence model for one-dimension vertical (1DV) oscillating bottom boundary layer in which a separation condition under a strong, adverse pressure gradient has been introduced and the diffusion and transition constants have been modified. This new turbulence model agrees better than the Wilcox original model with both a direct numerical simulation (DNS) of a pure oscillatory flow over a smooth bottom in the intermittently turbulent regime and with experimental data from Jensen et al. [1989] , who attained the fully turbulent regime for pure oscillatory flows. The new turbulence model is also found to agree better than the original one with experimental data of an oscillatory flow with current over a rough bottom by Dohmen-Janssen [1999] . In particular, the proposed model reproduces the secondary humps in the Reynolds stresses during the decelerating part of the wave cycle and the vertical phase lagging of the Reynolds stresses, two shortcomings of all previous modeling attempts. In addition, the model predicts suspension ejection events in the decelerating part of the wave cycle when it is coupled with a sediment concentration equation. Concentration measurements in the sheet flow layer give indication that these suspension ejection events do occur in practice.

Summary (2 min read)

Jump to: [1. Introduction] – [2.1. Basic Formulation] – [2.2. Modeling of Turbulent Separation Under the Effect of an Adverse Pressure Gradient] – [3. Pure Oscillatory Flow Over a Smooth Bottom] – [4. Oscillatory Flow Plus Current Over a] and [5. Conclusions]

1. Introduction

  • In coastal zones, the suspension associated to waves and currents in the bottom boundary layer can have an impact on both human activities and ecological equilibrium.
  • Moreover suspension can also affect directly the life cycle of some species and hence play a role in their population dynamics.
  • Similarly, when using the Wilcox [1992] transitional k-w turbulence model, that includes low-Reynolds-number effect, the eddy viscosity time series for oscillating boundary layers do not present any peak. [9].
  • Even though such a sophisticated model is beyond the scope of this paper, it is clear that the strong turbulence activity which takes place during the decelerating phases of the cycle should be taken into account since it contributes to put more sediment in suspension.

2.1. Basic Formulation

  • The basis of the Reynolds Averaged Navier-Stokes (R.A.N.S.) model the authors use to compute the turbulent bottom boundary layer under an oscillatory flow (with or without current) is the transitional k-w model devised by Wilcox [1992] in its 1DV formulation.
  • In addition, turbulence damping by stratification is introduced into the original Wilcox formulation through coupling terms between turbulence and the density field r(z, t) = r0 + C(z, t)(rs r0) resulting from the sediment suspension (r0 is the fluid density, rs is the sediment density and C(z, t) is the sediment concentration per volume).
  • The coupling terms are similar to those introduced by Lewellen [1977] in a k-L model.
  • Hence, Wilcox [1992] proposed values for RK = 6, Rb = 8 and s = s* = 0.5 that give the best agreement both with experiments and direct numerical simulations of steady boundary layers with and without adverse or favorable pressure gradient.

2.2. Modeling of Turbulent Separation Under the Effect of an Adverse Pressure Gradient

  • The authors now discuss the modeling of turbulence separation near flow reversal.
  • Hence, the authors suggest to model this wall friction enhancement before flow separation under the effect of the adverse pressure gradient for fully developed turbulence and rough walls only, as follows. [14].
  • Hence, to define the adverse pressure gradient in oscillatory flow, the authors should compare the pressure gradient action to the near-wall velocity.
  • In contrast, a 0.1 phase resolution is required to obtain converged computations with the separation condition. [17].
  • On Figure 2b, the authors show the computations with bsep = 20 for wvortex ranging from 30 to 3000 (usual values for wwall for this flow condition is 104).

3. Pure Oscillatory Flow Over a Smooth Bottom

  • Velocity , Reynolds stress and turbulent kinetic energy vertical profiles through the boundary layer at different phases during half oscillation are also plotted.
  • On Figure 6, the nondimensional bottom shear stress time series (bottom shear stress time series divided by the maximum bottom shear stress) computed using the original Wilcox model and the new one are plotted.
  • To compare the theoretical predictions with the experimental data, this figure should be compared to Figure 9 of Jensen et al.
  • It is then clear that in the original Wilcox model, the laminar-turbulent transition develops much quicker for Re larger than 3.3 104, whereas the new model with modified value for RK and Rb gives results closer to the measurements.

4. Oscillatory Flow Plus Current Over a

  • The k-W Model Versus Tunnel Experiments 4.1. Dohmen-Janssen [1999] ClearWater Experiments [27], also known as Rough Bottom.
  • In addition, the authors think the values they suggest for wwall and bsep to model secondary humps at the end of the decelerating phase will give physical and realistic results for usual field conditions since experiments G4 and G5 correspond to drastic field conditions.
  • Nevertheless, concentration peaks are also observed in time series measured using optical conductivity probes further from the bottom.
  • A significant discrepancy still remains between the predicted and the measured values.
  • The model predictions can be improved at all levels by taking into account the intergranular forces in the ‘‘sheet flow’’ layer (highly concentrated bottom layer).

5. Conclusions

  • A new transitional k-w model has been devised introducing a turbulent separation condition under adverse pressure gradient and modifying the diffusion and transition constants of the Wilcox [1992] original k-w transitional model.
  • The authors are thus able to reproduce the wall shear stress sharp increase, which takes place at transition in good agreement with Jensen et al. data.
  • The change of the diffusion constants improves also the description of the vertical distribution of both velocity and Reynolds stress compared to the original transitional Wilcox [1992] model.
  • This feature has never been reproduced in standard R.A.N.S. models.
  • This work was funded by the EC through a MAST-III project SEDMOC (contract MAS3-CT97-0115).

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Content maybe subject to copyright    Report

1DV bottom boundary layer modeling under combined wave and
current: Turbulent separation and phase lag effects
Katell Guizien,
1,4
Marjolein Dohmen-Janssen,
2
and Giovanna Vittori
3
Received 9 January 2002; revised 3 September 2002; accepted 21 November 2002; published 28 January 2003.
[1] On the basis of the Wilcox [1992] transitional k- w turbulence model, we propose a new
k-w turbulence model for one-dimension vertical (1DV) oscillating bottom boundary layer
in which a separation condition under a strong, adverse pressure gradient has been
introduced and the diffusion and transition constants have been modified. This new
turbulence model agrees better than the Wilcox original model with both a direct
numerical simulation (DNS) of a pure oscillatory flow over a smooth bottom in the
intermittently turbulent regime and with experimental data from Jensen et al. [1989], who
attained the fully turbulent regime for pure oscillatory flows. The new turbulence model is
also found to agree better than the original one with experimental data of an oscillatory
flow with current over a rough bottom by Dohmen-Janssen [1999]. In particular, the
proposed model reproduces the secondary humps in the Reynolds stresses during the
decelerating part of the wave cycle and the vertical phase lagging of the Reynolds stresses,
two shortcomings of all previous modeling attempts. In addition, the model predicts
suspension ejection events in the decelerating part of the wave cycle when it is coupled
with a sediment concentration equation. Concentration measurements in the sheet flow
layer give indication that these suspension ejection events do occur in practice.
INDEX
TERMS: 4211 Oceanography: General: Benthic boundary layers; 4560 Oceanography: Physical: Surface waves
and tides (1255); 4568 Oceanography: Physical: Turbulence, diffusion, and mixing processes; 4842
Oceanography: Biological and Chemical: Modeling; 4558 Oceanography: Physical: Sediment transport;
K
EYWORDS: turbulence, modeling, wave boundary layer, sediment dynamics
Citation: Guizien, K., M. Dohmen-Janssen, and G. Vittori, 1DV bottom boundary layer modeling under combined wave and current:
Turbulent separation and phase lag effects, J. Geophys. Res., 108(C1), 3016, doi:10.1029/2001JC001292, 2003.
1. Introduction
[2] In coastal zones, the suspension associated to waves
and currents in the bottom boundary layer can have an
impact on both human activities and ecological equilibrium.
Indeed, it is well known that suspension plays a major role in
sediment transport and affects human works and biological
species through morphodynamical changes, which may
affect the stability of the former and destroy the habitats of
the latter. Moreover suspension can also affect directly the
life cycle of some species and hence play a role in their
population dynamics. This is the case for instance for benthic
invertebrates with plan ktonic l arvae. Ind eed, the larvae
settlement on the bed may be limited by strong suspension
events and lead to dramatic cut in the population. Studying
the suspension dynamics under waves and currents is hence
of great interest, especially over flat bed since this corre-
sponds to the more severe hydrodynamical conditions.
[
3] As a conclusion of the MAST II G8-M Coastal
Morphodynamics European project, some shortcomings in
modeling sand transport by combined waves and currents
have been identified which are reported by Davies et al.
[1997]. In their paper, an intercomparison of experimental
data with four research sediment transport models under
combined waves and currents was presented . The four
models mainly differed in the complexity of the turbulence
closure schemes (from zero to two-equations) used to
compute the eddy-viscosity in the bottom turbulent boun-
dary layer. In Fredsøe’s [1984] model, a time-dependent
eddy viscosity is derived from integration of the momentum
equation over the wave boundary layer, assuming a loga-
rithmic velocity profile (zero-equation model). Ribberink
and Al Salem [1995] used a time- and height-dependent
eddy viscosity by extending Prandtl’s mixing length theory
to an unsteady flow (zero-equation model). Li and Davies
[1996] used a k-equation model with a similarity l-scaling
(one-equation model) and Huynh Than et al. [1994] used a
k-L model (two-equation model) to compute a time-varying
eddy visc osity. The concent rati on is computed from a
convection-diffusion equation in which vertical sediment
diffusivity is assumed to be equal to the time-dependent
eddy viscosit y, except in the Huynh Than et al. model where
JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 108, NO. C1, 3016, doi:10.1029/2001JC001292, 2003
1
Laboratoire des Ecoulements Ge´ophysiques et Industriels, Grenoble
Cedex 9, France.
2
Department of Civil Engineering, University of Twente, Enschede,
Netherlands.
3
Dipartimento di Ingegneria Ambientale, Universita` di Genova, Genoa,
Italy.
4
Now at Laboratoire d’Oce´anographie Biologique de Banyuls, Banyuls
sur Mer Cedex, France.
Copyright 2003 by the American Geophysical Union.
0148-0227/03/2001JC001292$09.00
16 - 1
turbulence damping is taken into account so that eddy
viscosity and sediment diffusivity are related through some
coupling terms. Despite the difference in the complexity of
the turbulence closure, all the models show similar short-
comings when predictions are compared to flat bed experi-
ments which correspond to strong wave plus current
conditions (‘‘sheet flow’’ regime).
[
4] All the models lead to underestimation of the phase
lag between concentration and velocity in the upper part of
an oscillatory boundary layer and to unreliable estimates of
sediment load p redictions. Recent experiments in clear
water (without sediment) by Dohmen-Janssen [1999] show
a relevant phase lag over depth in Reynolds stress time
series thus showing that the phase lag between concentration
and velocity is partially inherent to the oscillatory boundary
layer dynamics and not totally due to the sediment feedback
on the turbulence structure. Therefore, efforts should be
done to improve turbulence modeling for oscillatory boun-
dary layers before working on flow and sediment coupling.
[
5] In particular, none of the aforementioned models
reproduce correctly the phase lag between Reynolds stress
and velocity. This phase lag is related to the Reynolds stress
vertical decay in the region far from the wall: the quicker it
decays, the larger the phase lag is. In a recent paper, Sana
and Tanaka [2000] present a comparison between five low-
Reynolds-number k- models and the direct numerical
simulation (DNS) by Spalart and Baldwin [1989] for sinus-
oidal oscillatory flows over smooth beds. They show that
the Jones and Launder’s [1972] model provides better
predictions of transition initiation and of the Reynolds stress
vertical decay in the region far from the wall. These results
suggest that the introduction of low-Reynolds-number mod-
ifications could improve the modeling of phase lag between
Reynolds stress and velocity. However, it should also be
pointed out that Jones and Launder’s model underestimates
the peak value of the turbulent kinetic energy and over-
estimates the bottom shear stress enhancement after tran-
sition. It can be concluded that none of the low-Reynolds-
number modifications proposed in these five k-e models
enable to predict correctly the whole dynamics of the
oscillating boundary layer.
[
6] A second shortcoming of the models considered by
Davies et al. [1997] concerns concentration secondary
peaks which are sometimes observed near flow reversal in
experimental measurements close to the bottom [Katapodi
et al., 1994; Dohmen-Janssen, 1999] and are not repro-
duced by models. Although the very sharp concentration
peaks that show in the measurements close to the bottom
may be partly caused by the measuring technique, there are
indications that suspension ejection events really occur
before flow reversal (see section 4). These may be attributed
to shear instabilities in the wave boundary layer [Foster et
al., 1994].
[
7] The contribution of these secondary concent ration
peaks to the near-bed sediment load is limited, since they
occur at a time when the velocity is nearly zero. However,
the huge amount of sediment picked up from the bed around
flow reversal, especially for fine sand, may affect turbulence
and at the same time may be redistributed along time in the
upper suspension layer. Hence, these concentration secon-
dary peaks can be of great importance with respect to total
sediment load predictions. Besides, such suspension ejec-
tion events can play a crucial role in benthic life.
[
8] Savioli and Justesen [1996] proposed a modified
condition for the reference concentration that enables to
reproduce secondary peaks on the concentration time series
with a standard (without low-Reynolds-number effects) k-
model [Rodi, 1980] in a one-dimensional vertical (1DV)
fully rough turbulent oscillating boundary layer model,
Figure 1. Phase j definition along the oscillatory part of
the outer flow velocity ( –) and corresponding pressure
gradient (- -).
Figure 2. Phase-averaged Reynolds stress time series
obtained using the new k - w model for (a) b
sep
ranging from
4to40(w
vortex
= 300) and (b) w
vortex
ranging from 30 to
3000 (b
sep
= 20) (R
d
= 2179, R
e
=2.4 10
6
, A/k
N
= 3173).
16 - 2 GUIZIEN ET AL.: 1DV BOTTOM BOUNDARY LAYER MODELING UNDER COMBINED WAVE AND CURRENT
taking advantage of a narrow diffusivity peak just before
flow reversal. A much smaller narrow peak, is also present
near flow reversal in the eddy viscosity time series com-
puted using a standard k-w turbulence model [Wilcox, 1988],
whereas a k-L turbulence model [Huynh Than et al., 1994]
does not produce such peaks. However, although showing
discrepancies on the eddy viscosity time series, the three
turbulence models produce similar time series of the bottom
shear stress, without any significant increase near flow
reversal [Guizien et al., 2001]. In fact, differences in the
eddy viscosity time series are due to the closures of the
models, namely to the singularity in the behavior of the
eddy viscosity, that reads n
T
= k/w in the k-w model and
n
T
= 0.09 k
2
/ in the k- model. The singularity arises when k
and the other value w or approach zero, for instance when
the outer flow velocity decreases to zero during a wave
cycle. At that phase, t he instantaneous local Reynolds
number decreases rapidly and the eddy viscosity strongly
increases if the fully turbulent value for the model constants
is applied. In steady boundary layers, it is well known that
the constants used in k- standard models should be modified
using low-Reynolds-number damping function to avoid the
singular behavior of the eddy viscosity near the wall when
computing the viscous sublayer. It is worth noticing that, in
standard k-w models, the viscous sublayer can be easily
included for both smooth and rough bottom [Saffman, 1970],
avoiding this latter near-wall singularity. In addition, under
stationary conditions with an adverse pressure gradient and
for low-Rey nolds-numbers, standard k-w models perform
bett er than standard k- models [Wilcox,1998].Thisis
consistent with the fact that the near-reversal eddy viscosity
peak is smaller in the standard k-w computations than in the
standard k- computations and that a much smaller time step
(50 times smaller, strongly depending on the velocity ampli-
tude) is required to deal with the singularity in computations
with a standard k- model compa red to computations per-
formed with a standard k-w model. However, introducing
low-Reynolds-number effect in a k- turbulence model (e.g.,
Chien [1982] model, used by Thais et al. [1999]), the peak in
the eddy viscosity time series for an oscillating boundary
layer vanishes (L. Thais, personal communication, 1999).
Similarly, when using the Wilcox [1992] transitional k-w
turbulence model, that includes low-Reynolds-number
effect, the eddy viscosity time series for oscillating boundary
layers do not present any peak.
[
9] Recently, clear water experiments by Dohmen-Jans-
sen [1999] shed a new light on this question. During these
experiments, stronger turbulent activity was detected in the
Reynolds stress time series close to the wall in the decel-
erating part of the wave cycle. This turbulence enhancement
occurs at phases when the concentration secondary peaks
are observed for the same hydrodynamical conditions. It
should be outlined that fluctuat ions similar to the ones
measured by Dohmen-Janssen were observed by Sleath
[1987]. He also measured a 180 phase shift of the phase
of the Reynolds stress maximum at a certain height from the
bed and explained it by assuming the existence of jets of
fluids associated with vortex formation over the bottom
roughness. He suggested that these jets of fluid would
dominate the flow close to the wall whereas turbulence
would dominate far from it. This explanation clearly implies
that a d etailed modeling of rough oscillating boundary
layers should be three-dimensional and include a mecha-
nism for vortex generation by bottom roughness. Even
though such a sophisticated model is beyond the scope of
this paper, it is clear that the strong turbulence activity
which takes place during the decelerating phases of the
cycle should be taken into account since it contributes to put
more sediment in suspension. In this paper, starting from the
Wilcox [1992] transitional k-w model, a new transitional k-w
turbulence model is proposed in order to improve the 1DV
modeling of oscillating bottom boundary layers. A k-w
turbulence model is preferred to a k- one for its simplicity,
its ability to include the viscous sublayer and for its good
predictions under adverse pressure gradients, which occur
during the decelerating pha ses of the wave cycle. The
improvement brought to the Wilcox transitional k-w model
concerns vertical phase lagging and suspension ejection
events. The damping of turbulence by the stratification is
Figure 3. Velocity vertical profiles at different phases (a)
and bottom shear stress time evolution (b) computed by
DNS (...), the original Wilcox transitional k- w model (- -)
and the new k-w model (—) for a sinusoidal outer flow U =
U
0
sin(2pt/T ) with T =4s,U
0
= 1.1 m/s over a smooth
bottom (R
d
= 1241, R
e
=7.7 10
5
).
GUIZIEN ET AL.: 1DV BOTTOM BOUNDARY LAYER MODELING UNDER COMBINED WAVE AND CURRENT 16 - 3
Figure 4. Reynolds stress vertical profiles at different phases: (a) j = 45,(b)j =0,(c)j =45, and
(d) j =90 computed by DNS (...), the original Wilcox transitional k-w model (- -) and the new k-w
model (—) for a sinusoidal outer flow U = U
0
sin(2pt/T ) with T =4s,U
0
= 1.1 m/s over a smooth bottom
(R
d
= 1241, R
e
=7.7 10
5
).
Figure 5. Turbulent kinetic energy vertical profiles at different phases: (a) j = 45,(b)j =0,(c)j =
45, and (d) j =90 computed by DNS (...), the original Wilcox transitional k-w model (- -), and the new
k-w model (—) for a sinusoidal outer flow U = U
0
sin(2pt/T) with T =4s,U
0
= 1.1 cm/s over a smooth
bottom (R
d
= 1241, R
e
=7.7 10
5
).
16 - 4 GUIZIEN ET AL.: 1DV BOTTOM BOUNDARY LAYER MODELING UNDER COMBINED WAVE AND CURRENT
also introduced. The model is presented in section 2. The
ability of the new model to predict laminar-turbulent tran-
sition is tested for a pure oscillatory flow over a smooth
bottom by comparison with direct numerical simulations in
section 3.1 and with the experimental data from Jensen et
al. [1989] in section 3.2. The model is then compared with
experimental data in the rough turbulent regime for an
oscillatory flow plus current in section 4.1 [Dohmen-Jans-
sen, 1999]. Finally, concentration predictions corresponding
to these latter hydrodynamical conditions are described in
section 4.2.
2. The New k-W Model
2.1. Basic Formulation
[
10] The basis of the Reynolds Averaged Navier-Stokes
(R.A.N.S.) model we use to compute the turbulent bottom
boundary layer under an oscillatory flow (with or without
current) is the transitional k-w model devised by Wilcox
[1992] in its 1DV formulation. In addition, turbulence
damping by stratification is introduced into the original
Wilcox formulation through coupling terms between turbu-
lence and the density field r(z, t)=r
0
+ C(z, t)(r
s
r
0
)
resulting f rom the sediment susp ension (r
0
is the fluid
density, r
s
is the sediment density and C(z, t) is the sediment
concentration per volume). The coupling terms are similar
to those introduced by Lewellen [1977] in a k-L model. The
hydrodynamical model (i.e., without sediment) is easily
retrieved taking @r/@z =0.
[
11] The horizontal velocity u inside the boundary layer,
the turbulent kinetic energy k and the energy dissipation rate
w fulfill the following set of equations (1) –(6), where U is
the horizontal velocity outside the boundary layer (outer
flow) and
@
P
@x
is the mean pressure gradient generating the
current (note that for pure oscillatory flow,
@
P
@x
¼ 0). In this
1DV for mulatio n, we assume n o x-dependence for all
averaged quantities (no horizontal convective or diffusive
transport) and no vertical velocity at the top of the boundary
layer. These assumptions correspond strictly to the tunnel
experiment conditions we will compare with in the next
sections.
@u
@t
¼
1
r
0
@
P
@x
þ
@U
@t
þ
@
@z
n þ n
t
ðÞ
@u
@z

ð1Þ
@k
@t
¼ n
t
@u
@z

2
b*kw þ
@
@z
n þ s*n
t
ðÞ
@k
@z

þ
g
r
0
g
t
@r
@z
ð2Þ
@w
@t
¼an
t
w
k
@u
@z

2
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
production
bw
2
|{z}
dissipation
þ
@
@z
nþsn
t
ðÞ
@w
@z

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl}
diffusion
þc
0
w
2k
g
r
0
g
t
@r
@z
|fflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflffl}
buoyancy
ð3Þ
n
t
¼ a*
k
w
1 C
3
1 C
1
ðÞ1 C
2
ðÞ
ð4Þ
g
t
¼ n
t
1 C
2
1 C
3
ðÞ
ð5Þ
¼ 2
g
r
0
dr
dz
4
w
2
ð6Þ
with
a* ¼
a
0
*
þ Re
T
=R
K
1 þ Re
T
=R
K
; a ¼
13
25
a
0
þ Re
T
=R
w
1 þ Re
T
=R
w
a*ðÞ
1
;
b* ¼
9
100
4=15 þ Re
T
=R
b

4
1 þ Re
T
=R
b

4
where Re
T
¼
k
nw
; b ¼ b
0
¼
9
125
; a
0
*
¼
b
0
3
; a
0
¼
1
9
, R
w
= 2.95,
and c
0
= 0.8. It should be recalled here that, unlike most of
the above coefficients, no simple argument can be found to
estimate the values for s, s*, R
K
and R
b
. For given values
for R
K
and R
b
, there is a unique value of R
w
that yields the
value measured by Nikuradse of the constant appearing in
the law of the wall for smooth wall C
w
= 5.0. Hence, Wilcox
[1992] proposed values for R
K
=6,R
b
= 8 and s = s*=0.5
that give the best agreement both with experiments and
direct numerical simulations of steady boun dary layers with
and without adverse or favorable pressure gradient.
However, he already outlined that taking a smaller value
for s* should improve the model’s prediction for boundary
layers with variable pressure gradient. Hence, on the basis
of a preliminary analysis of the performances of the model
we suggest to use the following values for oscillatory
boundary layers (oscillatory pressure gradient): s = 0.8, s*=
0.375, R
K
= 20 and R
b
= 27. The original value for R
w
=
2.95 is kept and gives a constant for the law of the wall
C
w
= 7.6 for a steady boundary layer in the smooth regime.
These values provide better predictions than the values
Figure 6. Half-period bottom shear stress time series
showing laminar-turbulent transition for increasing Rey-
nolds number predicted by the original Wilcox transitional
k-w model (- -) and the new k-w model (—) for a sinusoidal
outer flow over a smooth bottom.
GUIZIEN ET AL.: 1DV BOTTOM BOUNDARY LAYER MODELING UNDER COMBINED WAVE AND CURRENT 16 - 5
Citations
More filters
Book•
The Turbulent Ocean

[...]

S. A. Thorpe1•
Bangor University1
01 Jan 2005
TL;DR: The Turbulent Ocean as discussed by the authors describes the principal dynamic processes that control the distribution of turbulence, its dissipation of kinetic energy and its effects on the dispersion of properties such as heat, salinity, and dissolved or suspended matter in the deep ocean, the shallow coastal and the continental shelf seas.
Abstract: The subject of ocean turbulence is in a state of discovery and development with many intellectual challenges. This book describes the principal dynamic processes that control the distribution of turbulence, its dissipation of kinetic energy and its effects on the dispersion of properties such as heat, salinity, and dissolved or suspended matter in the deep ocean, the shallow coastal and the continental shelf seas. It focuses on the measurement of turbulence, and the consequences of turbulent motion in the oceanic boundary layers at the sea surface and near the seabed. Processes are illustrated by examples of laboratory experiments and field observations. The Turbulent Ocean provides an excellent resource for senior undergraduate and graduate courses, as well as an introduction and general overview for researchers. It will be of interest to all those involved in the study of fluid motion, in particular geophysical fluid mechanics, meteorology and the dynamics of lakes.

380 citations

Journal Article•DOI•
Sand Motion induced by oscillatory flows: sheet flow and vortex ripples

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Jan S. Ribberink, Jebbe J. van der Werf, T. O' Donoghue1, Wael Hassan•
University of Aberdeen1
25 Jun 2008-Journal of Turbulence
TL;DR: In this article, the wave-related sand transport is still very difficult to predict due to the complexity of its underlying processes, which mainly take place in a thin layer near the sea bed in the wave boundary layer.
Abstract: Shoaling short gravity waves at sea approaching the shore become asymmetric and are able to generate a net resulting sand transport in cross-shore direction (on-shore-offshore transport). The wave-related sand transport is still very difficult to predict due to the complexity of its underlying processes, which mainly take place in a thin layer near the sea bed in the wave boundary layer (thickness of order centimeters). The development of models for cross-shore sand transport heavily relies on experimental lab research, especially as taking place in large oscillating water tunnels (see, e.g., Nielsen, 1992). In oscillating water tunnels the near-bed horizontal orbital velocity, as induced by short gravity waves, can be simulated above fixed or mobile sandy beds (for a detailed description, see, e.g., Ribberink and Al-Salem, 1994). It should be realized that the vertical orbital flow and relatively small wave-induced residual flows as streaming and drift are not reproduced in flow tunnels. Research aimed at their contribution to the net sediment motion under surface waves is still ongoing (see Ribberink et al., 2000).

120 citations

Cites background or methods from "1DV bottom boundary layer modeling ..."

  • ...(ii) The effects of high sediment concentration on flow turbulence are not modelled [17, 39, 53] or turbulence suppression is modelled in a simple way by adding a buoyancy term in the kinetic energy equation [36, 54, 55]....

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  • ...[54] using a k–ω model and by Holmedal et al....

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  • ...[54] propose a new transitional k–ω model to capture the concentration peaks observed to occur near flow reversal (Section 2....

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Journal Article•DOI•
Variation in Serripes groenlandicus (Bivalvia) growth in a Norwegian high-Arctic fjord : evidence for local- and large-scale climatic forcing

[...]

William G. Ambrose1, William G. Ambrose2, Michael L. Carroll, Michael Greenacre3, Simon R. Thorrold2, Kelton W. McMahon1, Kelton W. McMahon2 •
Bates College1, Woods Hole Oceanographic Institution2, Pompeu Fabra University3
01 Sep 2006-Global Change Biology
TL;DR: In this article, the author's version of the work is posted here by permission of Blackwell for personal use, not for redistribution, and the definitive version was published in Global Change Biology 12 (2006): 1595-1607, doi:10.1111/j.1365-2486.2006.01181.x
Abstract: Author Posting. © Blackwell, 2006. This is the author's version of the work. It is posted here by permission of Blackwell for personal use, not for redistribution. The definitive version was published in Global Change Biology 12 (2006): 1595-1607, doi:10.1111/j.1365-2486.2006.01181.x.

97 citations

Journal Article•DOI•
SedFoam-2.0: a 3-D two-phase flow numerical model for sediment transport

[...]

Julien Chauchat1, Zhen Cheng2, Zhen Cheng3, Tim Nagel1, Cyrille Bonamy1, Tian-Jian Hsu3 •
University of Grenoble1, Woods Hole Oceanographic Institution2, University of Delaware3
30 Nov 2017-Geoscientific Model Development Discussions
TL;DR: SedFoam-2.0 as mentioned in this paper is a three-dimensional two-phase flow solver for sediment transport applications, which can deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.
Abstract: . In this paper, a three-dimensional two-phase flow solver, SedFoam-2.0, is presented for sediment transport applications. The solver is extended from twoPhaseEulerFoam available in the 2.1.0 release of the open-source CFD (computational fluid dynamics) toolbox OpenFOAM. In this approach the sediment phase is modeled as a continuum, and constitutive laws have to be prescribed for the sediment stresses. In the proposed solver, two different intergranular stress models are implemented: the kinetic theory of granular flows and the dense granular flow rheology μ(I). For the fluid stress, laminar or turbulent flow regimes can be simulated and three different turbulence models are available for sediment transport: a simple mixing length model (one-dimensional configuration only), a k − e, and a k − ω model. The numerical implementation is demonstrated on four test cases: sedimentation of suspended particles, laminar bed load, sheet flow, and scour at an apron. These test cases illustrate the capabilities of SedFoam-2.0 to deal with complex turbulent sediment transport problems with different combinations of intergranular stress and turbulence models.

89 citations

Cites methods or result from "1DV bottom boundary layer modeling ..."

  • ...It is well-known that the original k− model has been derived for high Reynolds number flows and is not very accurate to describe transitional flows such as the situation of the flow reversal in a wave boundary layer (Guizien et al., 2003). For this situation and for near-wall treatment, the k−ω model is more suitable and more stable than the k− model (Guizien et al., 2003). Another physical situation in which a k−ω model works better than a k− model is in the presence of an adverse pressure gradient such as the downward facing step or at the upstream side of an obstacle (Menter, 1994; Wilcox, 2008). In order to test the influence of the turbulence model, a two-phase k−ω model is introduced in the present contribution, which is very similar to those of Jha and Bombardelli (2009) and Amoudry (2014)....

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  • ...It is well-known that the original k− model has been derived for high Reynolds number flows and is not very accurate to describe transitional flows such as the situation of the flow reversal in a wave boundary layer (Guizien et al., 2003). For this situation and for near-wall treatment, the k−ω model is more suitable and more stable than the k− model (Guizien et al., 2003). Another physical situation in which a k−ω model works better than a k− model is in the presence of an adverse pressure gradient such as the downward facing step or at the upstream side of an obstacle (Menter, 1994; Wilcox, 2008). In order to test the influence of the turbulence model, a two-phase k−ω model is introduced in the present contribution, which is very similar to those of Jha and Bombardelli (2009) and Amoudry (2014). The turbulent eddy viscosity ν t is calculated as...

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Journal Article•DOI•
Two-phase model for sand transport in sheet flow regime

[...]

Laurent O. Amoudry1, Tian-Jian Hsu2, Philip L.-F. Liu1, Philip L.-F. Liu3•
Cornell University1, University of Florida2, National Central University3
01 Mar 2008-Journal of Geophysical Research
TL;DR: In this paper, a two-phase model for sand transport in sheet flow regime is introduced, which uses a collisional theory and a k − ǫ fluid turbulence closure to respectively model the sediment and fluid phase stresses.
Abstract: [1] We introduce a two-phase model for sand transport in sheet flow regime. This model uses a collisional theory and a k – ɛ fluid turbulence closure to respectively model the sediment and fluid phase stresses. The sediment stress closure adopts a balance equation of sediment particle fluctuation energy based on kinetic theory that incorporates two-way interactions between fluid and sediment phases. The fluid turbulence closure also considers the two-way interaction between fluid turbulence and sand particles. Model-data comparisons for the sheet layer for oscillatory flows in a U-tube and for open channel flows demonstrate the model's predictive skill. For steady open channel flows the fluid phase velocity follows closely the law of wall (i.e., the log-profile) in which the von Karman constant is reduced and the equivalent roughness is increased, compared to the clear fluid flow conditions. The model also provides information in the near-bed region where the transition from the solid-like to the fluid-like behavior of sediment particles is resolved and both the bed load layer thickness and bed load transport rate can be evaluated. For unsteady flows, this model can predict time evolutions for sediment transport throughout the water column.

83 citations

Additional excerpts

  • ...All these features are typical of oscillatory wave-current boundary layers and have been observed in clear fluids both experimentally [e.g., Jensen et al., 1989] and numerically [e.g., Guizien et al., 2003 ]....

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References
More filters
Journal Article•DOI•
The nonlinear evolution of high-frequency resonant-triad waves in an oscillatory Stokes layer at high Reynolds number

[...]

Xuesong Wu1•
Imperial College London1
01 Dec 1992-Journal of Fluid Mechanics
TL;DR: In this paper, the authors studied the nonlinear evolution of high-frequency disturbances in high-Reynolds-number Stokes layers and showed that the growth rate of the disturbance is controlled by nonlinear interactions inside critical layers.
Abstract: The nonlinear evolution of high-frequency disturbances in high-Reynolds-number Stokes layers is studied. The disturbances are composed of a two-dimensional wave (2α, 0) of magnitude δ, and a pair of oblique waves (α, ± β) of magnitude e, where α, β are the streamwise and spanwise wavenumbers respectively. We assume that β = √3α so that the waves form a resonant triad when they are nearly neutral. It is shown that the growth rate of the disturbance is controlled by nonlinear interactions inside ‘critical layers’. In order for there to be a nonlinear feedback mechanism between the two-dimensional and the three-dimensional waves, the former is required to have a smaller magnitude than the latter, namely .As in Goldstein & Lee (1992), the amplitude equations turn out to be significantly different from those of Raetz (1959), Craik (1971) and Smith & Stewart (1987) in two respects. Firstly, they are integro-differential equations, i.e. the local growth rate depends on the whole history of the evolution. Secondly the back reaction of the oblique waves on the two-dimensional wave is represented by two cubic terms and one quartic term, rather than by one quadratic term. Our numerical investigations show that the amplitudes of the two- and three-dimensional waves can develop a finite-time singularity, a result of some importance. The structure of the finite-time singularity is identified, and it is found that the two-dimensional wave has a ‘more singular’ structure than the three-dimensional waves. The finite-time singularity implies that explosive growth is induced by nonlinear effects. We suggest that this nonlinear blow-up of high-frequency disturbances is related to the bursting phenomena observed in oscillatory Stokes layers and can lead to transition to turbulence.

59 citations

"1DV bottom boundary layer modeling ..." refers background in this paper

  • ...In the laminar regime, the presence of an inflection point is associated to instability and to transition to turbulence [Foster et al., 1994; Wu, 1992]....

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Journal Article•DOI•
Towards Predicting Sediment Transport in Combined Wave-Current Flow

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Zhihong Li, Alan G. Davies
01 Jul 1996-Journal of Waterway Port Coastal and Ocean Engineering-asce
TL;DR: In this article, a 1DV grid model was developed for the prediction of sediment transport in combined wave-current flow under sheet flow conditions, and the model used a one-equation turbulence closure scheme to simulate vertical mixing processes, and a time-varying reference concentration as the bottom boundary condition for the suspended sediment layer.
Abstract: A one-dimensional, vertical (1DV) grid model has been developed for the prediction of sediment transport in combined wave-current flow under sheet flow conditions. The model uses a one-equation turbulence closure scheme to simulate vertical mixing processes, and a time-varying reference concentration as the bottom boundary condition for the suspended sediment layer. Comparison with recent experimental data shows that the model gives good predictions (within 30%) of the measured net sediment transport rates under different conditions. The results also demonstrate the importance of the “wave-related” contribution to the suspended transport, due to the unsteadiness in the velocity and sediment concentration fields. At certain elevations above the bed, the suspended flux may be in the direction opposite to that of the mean current as a result of the phase relationship between the horizontal velocity and sediment concentration.

46 citations

Journal Article•DOI•
Coupling between the California Current System and a coastal plain estuary in low riverflow conditions

[...]

Barbara M. Hickey1, Xuebin Zhang1, Neil S. Banas1•
University of Washington1
01 Oct 2002-Journal of Geophysical Research
TL;DR: In this paper, the authors examine water properties and circulation patterns in a partially mixed coastal plain estuary during a low runoff period and demonstrate that variability is significant (up to 3 psu, ∼2°C and 10 cm s−1 at 5 km from the estuary mouth) and that this variability is determined primarily by the variability in the coastal ocean rather than by estuarine processes such as changes in riverflow or neap-spring variation in mixing.
Abstract: [1] Willapa Bay, a partially mixed coastal plain estuary, is located on the shoreward side of a narrow, deep continental shelf whose water properties fluctuate on several day scales in response to alternating periods of upwelling and downwelling. Hydrographic surveys as well as water property and velocity time series at a number of sites both within the estuary and on the adjacent coast are used to examine water property and circulation patterns in the estuary during a low runoff period. The data demonstrate that variability is significant (up to 3 psu, ∼2°C and 10 cm s−1 at 5 km from the estuary mouth) and that this variability is determined primarily by the variability in the coastal ocean rather than by estuarine processes such as changes in riverflow or neap-spring variation in mixing. Density changes near the mouth of the estuary that result from upwelling or downwelling of coastal water are consistent with transmission to the estuary primarily through a gravity current mechanism, which modifies the along-estuary density gradient and hence the gravitational circulation within the estuary. Tidal stirring is likely also important to the modification of estuary water properties. New water moves up the estuary at a rate on the order of 10 cm s−1. Associated Eulerian residual velocity fluctuations propagate up estuary about 50% faster than water properties, indicating that up-estuary transmission of the ocean water perturbation may also have internal wave-like characteristics. The modulations in estuarine circulation and water properties lag local wind stress fluctuations (hence upwelling or downwelling) by more than a day near the estuary mouth and several days farther up the estuary.

35 citations

The remarkable ability of turbulence model equations to describe transition

[...]

David C. Wilcox
01 Jan 1992
TL;DR: In this paper, the k-omega turbulence model was used to predict flow instabilities from laminar flow into the turbulent flow regime, and the model equations accurately predicted transition for an incompressible flat-plate boundary layer.
Abstract: This paper demonstrates how well the k-omega turbulence model describes the nonlinear growth of flow instabilities from laminar flow into the turbulent flow regime. Viscous modifications are proposed for the k-omega model that yield close agreement with measurements and with Direct Numerical Simulation results for channel and pipe flow. These modifications permit prediction of subtle sublayer details such as maximum dissipation at the surface, k approximately y(exp 2) as y approaches 0, and the sharp peak value of k near the surface. With two transition specific closure coefficients, the model equations accurately predict transition for an incompressible flat-plate boundary layer. The analysis also shows why the k-epsilon model is so difficult to use for predicting transition.

35 citations

Journal Article•DOI•
Review of k-ε model to analyze oscillatory boundary layers

[...]

Ahmad Sana, Hitoshi Tanaka1•
Nanyang Technological University1
01 Sep 2000-Journal of Hydraulic Engineering
TL;DR: In this article, five versions of low Reynolds number k-e models including the original one have been tested against the DNS data for 1D oscillatory boundary layers; one with sinusoidal and another with flat-crested free-stream velocity variation.
Abstract: Five versions of low Reynolds number k-e models including the original one have been tested against the DNS data for 1D oscillatory boundary layers; one with sinusoidal and another with flat-crested free-stream velocity variation. The comparison has been made for the cross-stream velocity, turbulent kinetic energy, Reynolds stress, and wall shear stress. It is found that the original model is superior to the more recent models by virtue of its numerically desirable boundary conditions and accuracy of prediction for mean flow properties. A brief description about the wall-limiting behavior of important turbulent quantities is presented to recognize physically correct k-e models.

24 citations

"1DV bottom boundary layer modeling ..." refers background in this paper

  • ...In a recent paper, Sana and Tanaka [2000] present a comparison between five lowReynolds-number k- models and the direct numerical simulation (DNS) by Spalart and Baldwin [1989] for sinusoidal oscillatory flows over smooth beds....

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Related Papers (5)
Coastal Bottom Boundary Layers and Sediment Transport

[...]

21 Jul 1992
Peter Nielsen
Concentrations in oscillatory sheet flow for well sorted and graded sands

[...]

01 Jan 2004-Coastal Engineering
Tom O'Donoghue, Scott Wright
Turbulent oscillatory boundary layers at high Reynolds numbers

[...]

01 Sep 1989-Journal of Fluid Mechanics
B. L. Jensen, B. M. Sumer, Jørgen Fredsøe
Mechanics Of Coastal Sediment Transport

[...]

01 Nov 1992
Jørgen Fredsøe, Rolf Deigaard
Sheet flow and suspension of sand in oscillatory boundary layers

[...]

01 Jul 1995-Coastal Engineering
Jan S. Ribberink, Athmar Al-Salem
Frequently Asked Questions (1)
Q1. What have the authors contributed in "1dv bottom boundary layer modeling under combined wave and current: turbulent separation and phase lag effects" ?

On the basis of theWilcox [ 1992 ] transitional k-w turbulence model, the authors propose a new k-w turbulence model for one-dimension vertical ( 1DV ) oscillating bottom boundary layer in which a separation condition under a strong, adverse pressure gradient has been introduced and the diffusion and transition constants have been modified.