| Issue |
Math. Model. Nat. Phenom.
Volume 12, Number 1, 2017
Hamiltonian Systems
|
|
|---|---|---|
| Page(s) | 94 - 114 | |
| DOI | https://doi.org/10.1051/mmnp/201712106 | |
| Published online | 03 February 2017 | |
Nonlinear Analysis of Perturbed Rotating Whirlpools in the Ocean and Atmosphere
1
Department of Mathematics & Physics, University of Wisconsin-Parkside
Kenosha, WI 53141
2
Department of Mathematics and School of Mechanical Engineering, Purdue University
West Lafayette, IN 47907
* Corresponding author. E-mail: Ibragimo@uwp.edu
A non-linear, 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 ϒ 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.
Mathematics Subject Classification: 76E20 / 76E30 / 76U05 / 76T30
Key words: internal waves / effects of rotation / exact solutions / whirlpools / numerical analysis
© EDP Sciences, 2017
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