3.3 Wave-Enhanced Turbulence
3.3.1 Dimensional analysis
One of the important parameters of turbulence is the dissipation rate of
TKE, H. Some conclusions about the vertical profile of H in the near-surface
layer of the ocean can be made from dimensional analysis.
For an equilibrium surface wave spectrum, ignoring buoyancy, Earth’s
rotation, and capillary wave effects, the following functional dependence can
be hypothesized (Soloviev et al., 1988):
, ,
function u z g
H
,
(3.24)
where u is the friction velocity in the near-surface layer of the ocean, g is
the acceleration of gravity, and z is the depth (expressed in a wave-following
coordinate system (3.1) for instance). Standard dimensional analysis leads to
the following dependence:
3
2
/
/
z u
g z u
HN
\
,
(3.25)
where \ is a universal function of its nondimensional parameter
2
/
g z u .
The asymptote of (3.25) at z o f should be logarithmic layer law (3.4),
which corresponds to
1
\ { .
Figure 3-13a shows the data obtained by Soloviev et al. (1988) and
Thorpe (2003a) under conditions of developed seas (wave age
/
13
w
p
a
A c u ! ). For turbulence measurements, Soloviev et al. (1988) used
a free-rising profiler, while Thorpe et al. (2003a) employed an autonomous
underwater vehicle (AUV). In order to minimize the influence of
thermohaline stratification on the near-surface turbulence, only the data
obtained under conditions of surface wave breaking ( 10 6
U t m s
-1 ) are
analyzed in Figure 3-13a.
Though the nondimensional variables
2
/
g z u and
3
/
z u
HN
provide a
convenient reference system for the analysis of near-surface turbulence data,
this scaling may not work well under conditions of developing seas. The
latter conditions are typical for lakes and coastal regions with short fetch but
are also often observed in the open ocean due to changing wind patterns. The
wave breaking process and, hence, parameters of near-surface turbulence
depend on the stage of surface wave development.
A simple way to account for the effect of surface wave age on the nearsurface turbulence dissipation has been proposed by Terray et al. (1996).
These authors hypothesized that the proper nondimensional variables for the
Chapter 3: NEAR-SURFACE TURBULENCE
173
3.3.1 Dimensional analysis
One of the important parameters of turbulence is the dissipation rate of
TKE, H. Some conclusions about the vertical profile of H in the near-surface
layer of the ocean can be made from dimensional analysis.
For an equilibrium surface wave spectrum, ignoring buoyancy, Earth’s
rotation, and capillary wave effects, the following functional dependence can
be hypothesized (Soloviev et al., 1988):
, ,
function u z g
H
,
(3.24)
where u is the friction velocity in the near-surface layer of the ocean, g is
the acceleration of gravity, and z is the depth (expressed in a wave-following
coordinate system (3.1) for instance). Standard dimensional analysis leads to
the following dependence:
3
2
/
/
z u
g z u
HN
\
,
(3.25)
where \ is a universal function of its nondimensional parameter
2
/
g z u .
The asymptote of (3.25) at z o f should be logarithmic layer law (3.4),
which corresponds to
1
\ { .
Figure 3-13a shows the data obtained by Soloviev et al. (1988) and
Thorpe (2003a) under conditions of developed seas (wave age
/
13
w
p
a
A c u ! ). For turbulence measurements, Soloviev et al. (1988) used
a free-rising profiler, while Thorpe et al. (2003a) employed an autonomous
underwater vehicle (AUV). In order to minimize the influence of
thermohaline stratification on the near-surface turbulence, only the data
obtained under conditions of surface wave breaking ( 10 6
U t m s
-1 ) are
analyzed in Figure 3-13a.
Though the nondimensional variables
2
/
g z u and
3
/
z u
HN
provide a
convenient reference system for the analysis of near-surface turbulence data,
this scaling may not work well under conditions of developing seas. The
latter conditions are typical for lakes and coastal regions with short fetch but
are also often observed in the open ocean due to changing wind patterns. The
wave breaking process and, hence, parameters of near-surface turbulence
depend on the stage of surface wave development.
A simple way to account for the effect of surface wave age on the nearsurface turbulence dissipation has been proposed by Terray et al. (1996).
These authors hypothesized that the proper nondimensional variables for the
Chapter 3: NEAR-SURFACE TURBULENCE
173