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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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\textit{R. N. Ibragimov} and \textit{G. Lin}, Math. Model. Nat. Phenom. 12, No. 1, 94--114 (2017; Zbl 1445.76033)

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