Chapter 5. SPATIALLY-COHERENT STRUCTURES
The surface wind stress is an important source of vorticity in the surface
layer of the ocean. Vorticity in the surface layer of the ocean may also arise
from shear currents driven by horizontal pressure gradients, which are not
necessary directly related to the surface stress. The surface waves (that
develop due to a prolonged action of the wind stress on the sea surface)
perturb the vorticity field in the near-surface layer of the ocean. In particular,
surface waves stretch and rotate vortex lines. The rectified (i.e., irreversible)
effects of the waves arise from additional advection and stretching of mean
vorticity by the wave-induced Stokes drift (Leibovich and Ulrich, 1972).
The governing equations in the model for the rectified water motion
under the Boussinesq approximation are based on the assumption of constant
eddy diffusivity of momentum (Q T ) and heat (F T ) and are as follows
(Leibovich, 1977b):
2
2
,
,
0,
s
T
T
T
u u u
U curlu
g k
u
t
T z
u
w
t
z
u
S
D T Q
T
T
F T
w
u
w
w
w
w
w
G
G
G
G G
G
G
G
G
(5.58)
where
T z is the temperature distribution in the absence of circulations, T
is the perturbation of temperature, T
D is the coefficient of thermal
expansion, g is the acceleration of gravity, u
G is the mean velocity vector in
the current, and S is a modified pressure term that includes the mean
pressure as well as terms involving wave kinetic energy.
The boundary conditions for the equation system (5.58) are as follows:
2 / ;
0;
0;
0 at
0;
T
u
v
u
w
z
z
z
Q
T
w
w
w
w
(5.59)
0,
0 as
u
z
T
o
o
of
G
,
(5.60)
where u is the friction velocity in water. The ocean at the initial moment is
motionless, except that surface waves are present. The wind drift current
does not change in the longitudinal direction x. If the wave-mean current
interactions are ignored (which means that the currents may be specified in
advance), then the Stokes drift is given a priori; the system of equations
(5.58) is closed.
This model is able to address the problem of the generation of Langmuir
circulations from the motionless state. It meets the criteria of Craik and
375
The surface wind stress is an important source of vorticity in the surface
layer of the ocean. Vorticity in the surface layer of the ocean may also arise
from shear currents driven by horizontal pressure gradients, which are not
necessary directly related to the surface stress. The surface waves (that
develop due to a prolonged action of the wind stress on the sea surface)
perturb the vorticity field in the near-surface layer of the ocean. In particular,
surface waves stretch and rotate vortex lines. The rectified (i.e., irreversible)
effects of the waves arise from additional advection and stretching of mean
vorticity by the wave-induced Stokes drift (Leibovich and Ulrich, 1972).
The governing equations in the model for the rectified water motion
under the Boussinesq approximation are based on the assumption of constant
eddy diffusivity of momentum (Q T ) and heat (F T ) and are as follows
(Leibovich, 1977b):
2
2
,
,
0,
s
T
T
T
u u u
U curlu
g k
u
t
T z
u
w
t
z
u
S
D T Q
T
T
F T
w
u
w
w
w
w
w
G
G
G
G G
G
G
G
G
(5.58)
where
T z is the temperature distribution in the absence of circulations, T
is the perturbation of temperature, T
D is the coefficient of thermal
expansion, g is the acceleration of gravity, u
G is the mean velocity vector in
the current, and S is a modified pressure term that includes the mean
pressure as well as terms involving wave kinetic energy.
The boundary conditions for the equation system (5.58) are as follows:
2 / ;
0;
0;
0 at
0;
T
u
v
u
w
z
z
z
Q
T
w
w
w
w
(5.59)
0,
0 as
u
z
T
o
o
of
G
,
(5.60)
where u is the friction velocity in water. The ocean at the initial moment is
motionless, except that surface waves are present. The wind drift current
does not change in the longitudinal direction x. If the wave-mean current
interactions are ignored (which means that the currents may be specified in
advance), then the Stokes drift is given a priori; the system of equations
(5.58) is closed.
This model is able to address the problem of the generation of Langmuir
circulations from the motionless state. It meets the criteria of Craik and
375