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Nonlinear Whirlpools Versus Harmonic Waves in a Rotating Columnof Stratified Fluid

Published online by Cambridge University Press:  28 January 2013

N. H. Ibragimov  and
R. N. Ibragimov
N. H. Ibragimov
Affiliation:
Department of Mathematics and Science, Blekinge Institute of Technology, SE-371 79 Karlskrona, Sweden and Research Laboratory “Group analysis of mathematical models in natural sciences, technics and technology” Ufa State Aviation Technical University, 450000 Ufa, Russia
R. N. Ibragimov*
Affiliation:
Department of Mathematics University of Texas at Brownsville, TX 78520, USA
*
∗ Corresponding author. E-mail: [email protected]
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Abstract

Propagation of nonlinear baroclinic Kelvin waves in a rotating column of uniformlystratified fluid under the Boussinesq approximation is investigated. The model isconstrained by the Kelvin’s conjecture saying that the velocity component normal to theinterface between rotating fluid and surrounding medium (e.g. a seashore) is possibly zeroeverywhere in the domain of fluid motion, not only at the boundary. Three classes ofdistinctly different exact solutions for the nonlinear model are obtained. The obtainedsolutions are associated with symmetries of the Boussinesq model. It is shown that oneclass of the obtained solutions can be visualized as rotating whirlpools along which thepressure deviation from the mean state is zero, is positive inside and negative outside ofthe whirlpools. The angular velocity is zero at the center of the whirlpools and it ismonotonically increasing function of radius of the whirlpools.

Keywords

stratified rotating fluidsnonlinear Boussinesq modelexact solutions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 8 , Issue 1: Harmonic analysis , 2013 , pp. 122 - 131
Copyright
© EDP Sciences, 2013

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