Abstract

This study examines the turbulent stress anisotropy tensor based on the Lumley triangle technique and eigenvalues in wave–current combined flows. The invariant functions are also presented at a different vertical location from the bed to comprehend the level of anisotropy in the combined flow. The spectral variation of the ratio of momentum flux to the turbulent kinetic energy is examined and discussed in comparison to the canonical value. The combined wave–current data display spectral variation considerably smaller than the canonical value (≈ 0.3) through the spectral frequencies domain. To characterize the behaviors of eddies in the wave–current turbulent flow, the Taylor and Kolmogorov length and time scales were analyzed and discussed. Furthermore, to enumerate the degree of organization of complex eddy motions in the combined flow, the normalized Shannon entropy is also evaluated using a discrete probability distribution.

References

1.
Van Hoften
,
J. D. A.
, and
Karaki
,
S.
,
1976
, “
Interaction of Waves and a Turbulent Current
,”
Proceedings of International Conference on Coastal Engineering
,
New York
,
July 11–17
, ASCE, pp.
404
422
.
2.
Kemp
,
P. H.
, and
Simons
,
R. R.
,
1982
, “
The Interaction of Waves and a Turbulent Current: Waves Propagating With the Current
,”
J. Fluids Mech.
,
116
, pp.
227
250
. 10.1017/S0022112082000445
3.
Kemp
,
P. H.
, and
Simons
,
R. R.
,
1983
, “
The Interaction of Waves and a Turbulent Current: Waves Propagating Against the Current
,”
J. Fluids Mech.
,
130
, pp.
73
89
. 10.1017/S0022112083000981
4.
Klopman
,
G.
,
1994
, “
Vertical Structure of the Flow due to Waves and Current: Laser-Doppler Flow Measurements for Waves Following or Opposing a Current
,”
Delft Hydraul
,
Delft, The Netherlands
, Report No. H840.32.
5.
Umeyama
,
M.
,
2005
, “
Reynolds Stresses and Velocity Distributions in a Wave-Current Coexisting Environment
,”
J. Waterw. Port Coastal Ocean Eng.
,
131
(
5
), pp.
203
212
. 10.1061/(ASCE)0733-950X(2005)131:5(203)
6.
Umeyama
,
M.
,
2009
, “
Changes in Turbulent Flow Structure Under Combined Wave-Current Motions
,”
J. Waterw. Port Coastal Ocean Eng.
,
135
(
5
), pp.
213
227
. 10.1061/(ASCE)0733-950X(2009)135:5(213)
7.
Singh
,
S. K.
, and
Debnath
,
K.
,
2017
, “
Turbulent Characteristics of Flow Under Combined Wave-Current Motion
,”
ASME J. Offshore Mech. Arct. Eng.
,
139
(
2
), p.
021102
. 10.1115/1.4035139
8.
Groeneweg
,
J.
, and
Klopman
,
G.
,
1998
, “
Changes of the Mean Velocity Profiles in the Combined Wave–Current Motion in a GLM Formulation
,”
J. Fluids Mech.
,
370
, pp.
271
296
. 10.1017/S0022112098002018
9.
Groeneweg
,
J.
, and
Battjes
,
J.
,
2003
, “
Three-Dimensional Wave Effects on a Steady Current
,”
J. Fluids Mech.
,
478
, pp.
325
343
. 10.1017/S0022112002003476
10.
Teles
,
M. J.
,
Pires-Silva
,
A. A.
, and
Benoit
,
M.
,
2013
, “
Numerical Modelling of Wave Current Interactions at Local Scale
,”
Ocean Modell.
,
68
, pp.
72
87
. 10.1016/j.ocemod.2013.04.006
11.
Tambroni
,
N.
,
Blondeaux
,
P.
, and
Vittori
,
G.
,
2015
, “
A Simple Model of Wave-Current Interaction
,”
J. Fluids Mech.
,
775
, pp.
328
348
. 10.1017/jfm.2015.308
12.
Singh
,
S. K.
, and
Debnath
,
K.
,
2016
, “
Combined Effect of Wave and Current in Free Surface Turbulent Flow
,”
Ocean Eng.
,
127
, pp.
170
189
. 10.1016/j.oceaneng.2016.10.014
13.
Singh
,
S. K.
,
Raushan
,
P. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2019
, “
Effect of Surface Wave on Development of Turbulent Boundary Layer Over Train of rib Roughness
,”
ASME J. Offshore Mech. Arct. Eng.
,
141
(
6
), p.
061101
. 10.1115/1.4042939
14.
Singh
,
S. K.
,
Khait
,
A.
,
Raushan
,
P. K.
, and
Debnath
,
K.
,
2020
, “
Localized and Distributed Emery in Wave-Current Flow
,”
ASME J. Offshore Mech. Arct. Eng.
,
143
(
1
), p.
011202
. 10.1115/1.4047521
15.
Paul
,
A.
,
Raushan
,
P. K.
,
Singh
,
S. K.
, and
Debnath
,
K.
,
2020
, “
Organized Structure of Turbulence in Wave-Current Combined Flow Over Rough Surface Using Spatio-Temporal Averaging Approach
,”
J. Braz. Soc. Mech. Sci. Eng.
,
42
(
11
), pp.
1
17
. 10.1007/s40430-020-02695-7
16.
Raushan
,
P. K.
,
Singh
,
S. K.
, and
Debnath
,
K.
,
2020
, “
Turbulence Anisotropy With Higher-Order Moments in Flow Through Passive Grid Under Rigid Boundary Influence
,”
Proc. Inst. Mech. Eng. Part C J. Mech. Eng. Sci.
10.1177/0954406220969736
17.
Singh
,
S. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2015
, “
Turbulence Statistics of Wave–Current Flow Over a Submerged Cube
,”
J. Waterw. Port Coastal Ocean Eng.
,
142
(
3
), pp.
1
20
. 10.1061/(asce)ww.1943-5460.0000329
18.
Singh
,
S. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2016
, “
Spatially-Averaged Turbulent Flow Over Cubical Roughness in Wave-Current Co-Existing Environment
,”
Coastal Eng.
,
127
, pp.
170
189
. 10.1016/j.coastaleng.2016.04.013
19.
Goring
,
D. G.
, and
Nikora
,
V. I.
,
2002
, “
Despiking Acoustic Doppler Velocimeter Data
,”
J. Hydraul. Eng.
,
128
(
1
), pp.
117
126
. 10.1061/(ASCE)0733-9429(2002)128:1(117)
20.
Singh
,
S. K.
,
Raushan
,
P. K.
, and
Debnath
,
K.
,
2018
, “
Turbulent Characteristics of Pulsating Flow Over Hydraulically Smooth Surface
,”
Eur. J. Mech. B. Fluids
,
68C
, pp.
10
19
. 10.1016/j.euromechflu.2017.10.011
21.
Reynolds
,
W. C.
, and
Hussain
,
A. K. M. F.
,
1972
, “
The Mechanics of an Organized Wave in Turbulent Shear Flow. Part 3. Theoretical Models and Comparisons With Experiments
,”
J. Fluids Mech.
,
54
(
2
), pp.
263
288
. 10.1017/S0022112072000679
22.
Pope
,
S. B.
,
2000
, “
Turbulent Flows
”,
Cambridge University Press
,
Cambridge, MA
.
23.
Lumley
,
J. L.
, and
Newman
,
G. R.
,
1977
, “
The Return to Isotropy of Homogeneous Turbulence
,”
J. Fluids Mech.
,
82
(
1
), pp.
161
178
. 10.1017/S0022112077000585
24.
Alegre
,
D. M.
,
Alves
,
F. S.
,
Thompson
,
R. L.
,
Mitre
,
J. F.
, and
Sampaio
,
L. E. B.
,
2020
, “
The use of General Convected Time Derivative to Compute the Reynolds Stress Tensor for a Compressible Turbulent Flow
,”
J. Braz. Soc. Mech. Sci. Eng.
,
42
(
3
), p.
126
. 10.1007/s40430-020-2221-x
25.
Bomminayuni
,
S.
, and
Stoesser
,
T.
,
2011
, “
Turbulence Statistics in an Open-Channel Flow Over a Rough Bed
,”
J. Hydraul. Eng.
,
137
(
11
), pp.
1347
1358
. 10.1061/(ASCE)HY.1943-7900.0000454
26.
Stiperski
,
I.
, and
Calaf
,
M.
,
2018
, “
Dependence of Near-Surface Similarity Scaling on the Anisotropy of Atmospheric Turbulence
,”
Q. J. R. Meteorolog. Soc.
,
144
(
712
), pp.
641
657
. 10.1002/qj.3224
27.
Longo
,
S.
,
Clavero
,
M.
,
Chiapponi
,
L.
, and
Losada
,
M.
,
2017
, “
Invariants of Turbulence Reynolds Stress and of Dissipation Tensors in Regular Breaking Waves
,”
Water
,
9
(
11
), p.
893
. 10.3390/w9110893
28.
Wijesekera
,
H. W.
, and
Dillion
,
T. M.
,
1997
, “
Shannon Entropy as an Indicator of Age for Turbulent Overturns in the Ocean Thermoc Lines
,”
J. Geophys. Res.
,
102
, pp.
3279
3291
. 10.1029/96JC03605
29.
Mihailović
,
D.
,
Mimic
,
G.
,
Gualtier
,
P.
,
Arsenic
,
I.
, and
Gualtieri
,
C.
,
2017
, “
Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures
,”
Entropy
,
19
(
10
), pp.
2
14
. 10.3390/e19100519
30.
Tavoularis
,
S.
, and
Corrsin
,
S.
,
1981
, “
Experiments in Nearly Homogenous Turbulent Shear Flow With a Uniform Mean Temperature Gradient. Part 1
,”
J. Fluids Mech.
,
104
, pp.
311
347
. 10.1017/S0022112081002930
31.
Walter
,
R. K.
,
Nidzieko
,
N. J.
, and
Monismith
,
S. G.
,
2011
, “
Similarity Scaling of Turbulence Spectra and Cospectra in a Shallow Tidal Flow
,”
J. Geophys. Res.
,
116
, p.
C10
. 10.1029/2011jc007144
32.
Irwin
,
H. P. A. H.
,
1973
, “
Measurements in a Self-Preserving Plane Wall Jet in a Positive Pressure Gradient
,”
J. Fluids Mech.
,
61
(
1
), pp.
33
63
. 10.1017/S0022112073000558
33.
Murzyn
,
F.
, and
Bélorgey
,
M.
,
2005
, “
Experimental Investigation of the Grid-Generated Turbulence Features in a Free Surface Flow
,”
Exp. Therm. Fluid Sci.
,
29
(
8
), pp.
925
935
. 10.1016/j.expthermflusci.2005.02.002
34.
Venditti
,
J. G.
, and
Bauer
,
B. O.
,
2005
, “
Turbulent Flow Over a Dune: Green River Colorado
,”
Earth Surf. Processes Landforms
,
30
(
3
), pp.
289
304
. 10.1002/esp.1142
35.
Raushan
,
P. K.
,
Singh
,
S. K.
,
Debnath
,
K.
,
Mukhrjee
,
M.
, and
Mazumder
,
B. S.
,
2018
, “
Distribution of Turbulent Energy in Combined Wave-Current Flow
,”
Ocean. Eng.
,
127
, pp.
170
189
. 10.1016/j.oceaneng.2018.08.058
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