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Nonlinear analysis of perturbed rotating whirlpools in the Ocean and atmosphere. (English) Zbl 1445.76033

Summary: A nonlinear, uniformly stratified ocean model is used to investigate the stability and existence of perturbed rotating whirlpools that represent a certain class of exact solutions for the governing nonlinear equations describing the propagation of internal gravity waves in stratified media. A cut-off frequency is identified, beyond which the flow is completely stable to linear disturbances. An analysis close to cut-offs reveals the latitude-dependent distribution of eigenfrequencies of oscillatory and evanescent perturbations of whirlpools.

MSC:

76B55 Internal waves for incompressible inviscid fluids
76B15 Water waves, gravity waves; dispersion and scattering, nonlinear interaction
76U60 Geophysical flows
86A05 Hydrology, hydrography, oceanography
76E20 Stability and instability of geophysical and astrophysical flows
76E30 Nonlinear effects in hydrodynamic stability

Software:

DESOLVII
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References:

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