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(2010, personal communication) developed a numerical model of turbulence in poten-
tial waves. The model consists of three parts: fully nonlinear potential model of two-
dimensional (i.e. long-crested) waves (
Chalikov & Sheinin
,
2005
), LES three-dimensional
model based on full Reynolds equations with subgrid turbulence, and three-dimensional
model of evolution of subgrid turbulence. The last two modules are new and written in
cylindrical conformal coordinates. Small pertubations of the potential motion are intro-
duced and then allowed to develop as dictated by the theory. As such, this model does not
have tuning parameters and can be used for qualitative and even quantitative investigation
of the phenomenon.
In the absence of breaking (that is for waves with small steepness and transitional
Reynolds numbers - see discussion in
Section 7.5
), the turbulence in the model is strongly
intermittent because the time scale for dissipation is very short. It concentrates at the rear
face of the waves. This is what was also observed in laboratory experiments of
Babanin &
Haus
(
2009
) with such turbulence. Comparison of the volumetric dissipation rates pro-
duced by the model and those measured by
Babanin & Haus
(
2009
)aregivenin
Figure 9.10
.
Such dissipation rates
max
are plotted as a function of wave amplitude
a
, like
dis
in
Figure 7.24
. It is, however, not exactly the same property as
(
Diss
)
dis
in
Figure 7.24
and in
Babanin & Haus
(
2009
). Those were measured below the troughs of the highest
waves, i.e. always at some distance below the surface and even below the mean water level.
1.0E0
1.0E-2
1.0E-4
1.0E-6
1.0E-8
0.001
0.010
a
0.100
Figure 9.10 Maximal volumetric dissipation rates
max
(
Diss
)
versus wave amplitude
a
(Chalikov,
2010, personal communication, numerical model of non-breaking wave-induced turbulence in poten-
tial waves). The shaded area corresponds to the range of measurement and scatter of the observational
data of
Babanin & Haus
(
2009
)
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