Chapter 5. SPATIALLY-COHERENT STRUCTURES
Length
Time
(T d )
Wind-directed
component of rectified
current
Crosswind velocity
component of rectified
currents
k
-1
(Q T /V)
1/2 /aNu *
u *
2 /Q T N
( au * /Q T )(VQ T )
1/2
The Langmuir cells are produced via the vortex force as an inviscid
instability of the unidirectional current. The vortex force represented by
(5.61) in this case is balanced by a vertical pressure gradient. Assuming that
u s and u and the vortex force typically decrease monotonically with depth
below the surface, the joint effect of typical distributions of U s and u appears
to be analogous to a statically unstable density distribution (Leibovich,
1983). If dissipation is sufficiently weak, the rectilinear current could
become unstable. It is interesting that if the waves and current are opposed,
then the vortex force is stabilizing and Langmuir circulations cannot be
generated by the CL2 mechanism.
Table 5-3. Scalings for the Craik and Leibovich model of Langmuir circulations.
379
Figure 5-55. Sketch illustrating the Craik and Lebovich instability mechanism of Langmuircirculations generation. The Stokes drift is horizontal but decays in depth. Streamwise vorticity
is induced by the current. Variations of vortex force caused by the current perturbation create
torques leading to overturning. Reprinted from Leibovich (1983) with permission by Annual
Reviews www.annualreviews.org
Length
Time
(T d )
Wind-directed
component of rectified
current
Crosswind velocity
component of rectified
currents
k
-1
(Q T /V)
1/2 /aNu *
u *
2 /Q T N
( au * /Q T )(VQ T )
1/2
The Langmuir cells are produced via the vortex force as an inviscid
instability of the unidirectional current. The vortex force represented by
(5.61) in this case is balanced by a vertical pressure gradient. Assuming that
u s and u and the vortex force typically decrease monotonically with depth
below the surface, the joint effect of typical distributions of U s and u appears
to be analogous to a statically unstable density distribution (Leibovich,
1983). If dissipation is sufficiently weak, the rectilinear current could
become unstable. It is interesting that if the waves and current are opposed,
then the vortex force is stabilizing and Langmuir circulations cannot be
generated by the CL2 mechanism.
Table 5-3. Scalings for the Craik and Leibovich model of Langmuir circulations.
379
Figure 5-55. Sketch illustrating the Craik and Lebovich instability mechanism of Langmuircirculations generation. The Stokes drift is horizontal but decays in depth. Streamwise vorticity
is induced by the current. Variations of vortex force caused by the current perturbation create
torques leading to overturning. Reprinted from Leibovich (1983) with permission by Annual
Reviews www.annualreviews.org