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Editorial Type:
Article
Article Type:
Research Article

Stability of Free Surface Ekman Layers

George F. SpoonerOcean Dynamics Branch, Naval Research Laboratory, Washington, DC 20375

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Print Publication:
01 Apr 1983
DOI:
https://doi.org/10.1175/1520-0485(1983)013<0663:SOFSEL>2.0.CO;2
Page(s):
663–677
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Abstract

The stability of free surface, laminar Ekman layers is examined for both the homogeneous and the two-layer case. The eigenvalues of the homogeneous case depend upon the wavenumbers α and γ and the Reynolds number Re. Those of the two-layer case depend upon α, γ, Re, the depth of the top layer, and the parameter Fr* = gδ(ρ* − ρ)/(Us2ρ), where g is the acceleration of gravity, δ is the Ekman scaling depth, ρ and ρ* are the densities of the top and bottom layers, respectively, and Us, is the mean speed at the surface. The behavior of the inflection point mode and the parallel mode of instability is examined as a function of the independent parameters in both cases.

Abstract

The stability of free surface, laminar Ekman layers is examined for both the homogeneous and the two-layer case. The eigenvalues of the homogeneous case depend upon the wavenumbers α and γ and the Reynolds number Re. Those of the two-layer case depend upon α, γ, Re, the depth of the top layer, and the parameter Fr* = gδ(ρ* − ρ)/(Us2ρ), where g is the acceleration of gravity, δ is the Ekman scaling depth, ρ and ρ* are the densities of the top and bottom layers, respectively, and Us, is the mean speed at the surface. The behavior of the inflection point mode and the parallel mode of instability is examined as a function of the independent parameters in both cases.

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