This article is cited in 10 papers

PLASMA, HYDRO- AND GAS DYNAMICS

Blow-up instability in shallow water flows with horizontally-nonuniform density

V. P. Goncharov^a, V. I. Pavlov<sup>b

a</sup> A. M. Obukhov Institute of Atmospheric Physics, Russian Academy of Sciences
^b Université de Lille

Abstract: The mechanisms of instability, whose development leads to the occurrence of the collapse (blow up), have been studied in the scope of the rotating shallow water flows with horizontal density gradient. Analysis shows that collapses in such models are initiated by the Rayleigh–Taylor instability and two scenarios are possible. Both the scenarios evolve according to a power law $(t_{0}-t)^{\gamma}$, where $t_{0}$ is the collapse time, with $\gamma=-1,-2$, and $\gamma=-2/3,-1$ for the isotropic and anisotropic collapses, respectively. The rigorous criterion of collapse is found on the base of integrals of motion.

Received: 09.06.2012
Revised: 21.08.2012

Language: English

 English version: Journal of Experimental and Theoretical Physics Letters, 2012, 96:7, 427–431

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