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In fluid dynamics, the CraikâLeibovich (CL) vortex force describes a forcing of the mean flow through waveâcurrent interaction, specifically between the Stokes drift velocity and the mean-flow vorticity. The CL vortex force is used to explain the generation of Langmuir circulations by an instability mechanism. The CL vortex-force mechanism was derived and studied by Sidney Leibovich and Alex D. D. Craik in the 1970s and 80s, in their studies of Langmuir circulations (discovered by Irving Langmuir in the 1930s).
The CL vortex force is
with the ( Lagrangian) Stokes drift velocity and vorticity (i.e. the curl of the Eulerian mean-flow velocity ). Further is the fluid density and is the curl operator.
The CL vortex force finds its origins in the appearance of the Stokes drift in the convective acceleration terms in the mean momentum equation of the Euler equations or NavierâStokes equations. For constant density, the momentum equation (divided by the density ) is: [1]
with
The CL vortex force can be obtained by several means. Originally, Craik and Leibovich used perturbation theory. An easy way to derive it is through the generalized Lagrangian mean theory. [1] It can also be derived through a Hamiltonian mechanics description. [2]
This article includes a list of general
references, but it lacks sufficient corresponding
inline citations. (September 2022) |
In fluid dynamics, the CraikâLeibovich (CL) vortex force describes a forcing of the mean flow through waveâcurrent interaction, specifically between the Stokes drift velocity and the mean-flow vorticity. The CL vortex force is used to explain the generation of Langmuir circulations by an instability mechanism. The CL vortex-force mechanism was derived and studied by Sidney Leibovich and Alex D. D. Craik in the 1970s and 80s, in their studies of Langmuir circulations (discovered by Irving Langmuir in the 1930s).
The CL vortex force is
with the ( Lagrangian) Stokes drift velocity and vorticity (i.e. the curl of the Eulerian mean-flow velocity ). Further is the fluid density and is the curl operator.
The CL vortex force finds its origins in the appearance of the Stokes drift in the convective acceleration terms in the mean momentum equation of the Euler equations or NavierâStokes equations. For constant density, the momentum equation (divided by the density ) is: [1]
with
The CL vortex force can be obtained by several means. Originally, Craik and Leibovich used perturbation theory. An easy way to derive it is through the generalized Lagrangian mean theory. [1] It can also be derived through a Hamiltonian mechanics description. [2]