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Pis'ma v Zhurnal Èksperimental'noi i Teoreticheskoi Fiziki, 2012, Volume 96, Issue 7, Pages 474–478
(Mi jetpl3242)
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This article is cited in 10 scientific papers (total in 10 papers)
PLASMA, HYDRO- AND GAS DYNAMICS
Blow-up instability in shallow water flows with
horizontally-nonuniform density
V. P. Goncharova, V. I. Pavlovb a 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
Citation:
V. P. Goncharov, V. I. Pavlov, “Blow-up instability in shallow water flows with
horizontally-nonuniform density”, Pis'ma v Zh. Èksper. Teoret. Fiz., 96:7 (2012), 474–478; JETP Letters, 96:7 (2012), 427–431
Linking options:
https://www.mathnet.ru/eng/jetpl3242 https://www.mathnet.ru/eng/jetpl/v96/i7/p474
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Abstract page: | 218 | Full-text PDF : | 43 | References: | 41 | First page: | 16 |
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