Abstract

Evaluation of localized and distributed in time spectral energy in wave–current coexisting environment is investigated in this study. In order to understand the inherent characteristics of the flow under consideration, the Hilbert-Huang transform (HHT) is introduced to determine the instantaneous frequency corresponding to the maximum energy carrying by the velocity field. This frequency is associated with the timescale of the most energetic velocity fluctuations. The intrinsic mean frequency of the intrinsic mode function (IMF) is reduced with the increase in the IMF number. It was shown that the maximum energy is concentrated close to the center of the IMF series. The spectral characteristics obtained by the HHT are carefully compared with those obtained by more conventional Fourier and wavelet transform (FFT and WT, respectively). Addition of the surface wave component to the velocity field of the current-only case leads to the extension of the frequency range containing the dominant portion of the energy.

Issue Section:
Ocean Engineering
Keywords:
spectral energy, turbulence, wave–current, Hilbert-Huang transform, coastal engineering, hydrodynamics, ocean energy technology, ocean waves and associated statistics, wave mechanics and wave effects
Topics:
Flow (Dynamics), Waves, Surface waves (Fluid), Fluctuations (Physics), Turbulence

References

1.
Kemp
,
P. H.
, and
Simons
,
R. R.
,
1982
, “
The Interaction of Waves and a Turbulent Current: Waves Propagating With the Current
,”
J. Fluid Mech.
,
116
, pp.
227
–
250
. 10.1017/S0022112082000445
2.
Kemp
,
P. H.
, and
Simons
,
R. R.
,
1983
, “
The Interaction of Waves and a Turbulent Current: Waves Propagating Against the Current
,”
J. Fluid Mech.
,
130
, pp.
73
–
89
. 10.1017/S0022112083000981
3.
Klopman
,
G.
,
1994
, “Vertical Structure of the Flow due to Waves and Current: Laser-Doppler Flow Measurements for Waves Following or Opposing a Current,”
Rep No. H840.32, Delft Hydraul
,
Delft
,
The Netherlands
.
4.
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
5.
Groeneweg
,
J.
, and
Klopman
,
G.
,
1998
, “
Changes of the Mean Velocity Profiles in the Combined Wave–Current Motion in a GLM Formulation
,”
J. Fluid Mech.
,
370
, pp.
271
–
296
. 10.1017/S0022112098002018
6.
Groeneweg
,
J.
, and
Battjes
,
J.
,
2003
, “
Three-Dimensional Wave Effects on a Steady Current
,”
J. Fluid Mech.
,
478
, pp.
325
–
343
. 10.1017/S0022112002003476
7.
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)
8.
Teles
,
M. J.
,
Pires-Silva
,
A. A.
, and
Benoit
,
M.
,
2013
, “
Numerical Modelling of Wave Current Interactions at Local Scale
,”
Ocean Model.
,
68
, pp.
72
–
87
. 10.1016/j.ocemod.2013.04.006
9.
Zhang
,
J. S.
,
Zhang
,
Y.
,
Jeng
,
D. S.
,
Liu
,
P. L. F.
, and
Zhang
,
C.
,
2014
, “
Numerical Simulation of Wave-Current Interaction Using RANS Solver
,”
Ocean Eng.
,
75
, pp.
157
–
164
. 10.1016/j.oceaneng.2013.10.014
10.
Jiang
,
J. Y.
,
Street
,
R. L.
, and
Klotz
,
S. P.
,
1990
, “
A Study of Wave-Turbulence Interaction by use of Nonlinear Water Wave Decomposition
,”
J. Geophys. Res.
,
95
(
C9
), pp.
16037
–
16054
. 10.1029/JC095iC09p16037
11.
Singh
,
S. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2015
, “
Turbulence Statistics of Wave–Current Flow Over a Submerged Cube
,”
ASCE J. Waterw. Port Coastal Ocean Eng.
,
142
(
3
), pp.
1
–
20
. 10.1061/(asce)ww.1943-5460.0000329
12.
Ma
,
Y. X.
,
Dong
,
G. H.
, and
Ma
,
X. Z.
,
2011
, “
Separation of Obliquely Incident and Reflected Irregular Waves by the Morlet Wavelet Transform
,”
Coastal Eng.
,
58
(
8
), pp.
761
–
766
. 10.1016/j.coastaleng.2011.03.014
13.
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
14.
Singh
,
S. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2016
, “
Spatially-Averaged Turbulent Flow Over Cubical Roughness in Wave-Current Co-existing Environment
,”
Coast Eng.
,
127
, pp.
170
–
189
. 10.1016/j.coastaleng.2016.04.013
15.
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)
16.
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
17.
Raushan
,
P. K.
,
Singh
,
S. K.
, and
Debnath
,
K.
,
2019
, “
Grid-generated Turbulence in Pulsating Flow Under the Rigid Boundary Influence
,”
Eur. J. Mech. B Fluids
,
78
, pp.
291
–
305
. 10.1016/j.euromechflu.2019.08.012
18.
Singh
,
S. K.
,
Raushan
,
P. K.
, and
Debnath
,
K.
,
2018
, “
Combined Effect of Wave and Current in Rough Bed Free Surface Flow
,”
Ocean Eng.
,
160
, pp.
20
–
32
. 10.1016/j.oceaneng.2018.04.055
19.
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
20.
Farge
,
M.
,
1992
, “
Wavelet Transforms and Their Applications to Turbulence
,”
Annu. Rev. Fluid Mech.
,
24
(
1
), pp.
395
–
457
. 10.1146/annurev.fl.24.010192.002143
21.
Su
,
B.
,
Yin
,
Y.
,
Li
,
S.
,
Guo
,
Z.
,
Wang
,
Q.
, and
Lin
,
M.
,
2018
, “
Wavelet Analysis on the Turbulent Flow Structure of a T-Junction
,”
Int. J. Heat Fluid Flow
,
73
, pp.
124
–
142
. 10.1016/j.ijheatfluidflow.2018.07.008
22.
Chernyshov
,
P.
,
Vrecica
,
T.
, and
Tolendo
,
Y.
,
2018
, “
Inversion of Nearshore X-Band Radar Images to Sea Surface Elevation Maps
,”
Remote Sens.
,
10
(
12
), p.
1919
. 10.3390/rs10121919
23.
Huang
,
N. E.
,
Long
,
S. R.
, and
Shen
,
Z.
,
1996
, “
The Mechanism for Frequency Downshift in Nonlinear Wave Evolution
,”
Adv. Appl. Mech.
,
32
, pp.
59
–
111
. 10.1016/S0065-2156(08)70076-0
24.
Huang
,
N. E.
,
Shen
,
Z.
, and
Long
,
S. R.
,
1999
, “
A New View of Nonlinear Water Waves: The Hilbert Spectrum
,”
Annu. Rev. Fluid Mech.
,
31
(
1
), pp.
417
–
57
. 10.1146/annurev.fluid.31.1.417
25.
Huang
,
N. E.
,
Shen
,
Z.
,
Long
,
S. R.
,
Wu
,
M. C.
,
Shih
,
H. H.
,
Zheng
,
Q.
,
Yen
,
N. C.
,
Tung
,
C. C.
, and
Liu
,
H. H.
,
1998
, “
The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Non-Stationary Time Series Analysis
,”
Proc. R Soc. London Ser. A
,
454
(
1971
), pp.
903
–
995
. 10.1098/rspa.1998.0193
26.
Li
,
F. C.
, and
Ting
,
C. L.
,
2012
, “
Separation of Free and Bound Harmonics in Waves
,”
Coastal Eng.
,
67
, pp.
29
–
40
. 10.1016/j.coastaleng.2012.04.003
27.
Li
,
H.
, and
Nozaki
,
T.
,
1995
, “
Wavelet Analysis for the Plane Turbulent Jet: Analysis of Large Eddy Structure
,”
JSME Int. J. Ser. B Fluids Therm. Eng.
,
38
(
4
), pp.
525
–
531
. 10.1299/jsmeb.38.525
28.
Singh
,
S. K.
,
Debnath
,
K.
, and
Mazumder
,
B. S.
,
2017
, “
Turbulence Over Cube-Mounted Rough Bed Using Spatio-Temporal Averaging Approach
,”
Can. J. Civ. Eng.
,
44
(
7
), pp.
504
–
517
. 10.1139/cjce-2016-0461
29.
Wu
,
Z.
, and
Huang
,
N. E.
,
2004
, “
A Study of the Characteristics of White Noise Using the Empirical Mode Decomposition Method
,”
Proc. R. Soc. Ser. A
,
460
(
2046
), pp.
1597
–
1611
. 10.1098/rspa.2003.1221
30.
Wei
,
W.
,
Schmitt
,
F.
,
Huang
,
Y.
, and
Zhang
,
H.
,
2016
, “
The Analyses of Turbulence Characteristics in the Atmospheric Surface Layer Using Arbitrary-Order Hilbert Spectra
,”
Boundary-Layer Meteorol.
,
159
(
2
), pp.
391
–
406
. 10.1007/s10546-015-0122-9
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