Blow-up instability in shallow water flows with horizontally-nonuniform density
V. P. Goncharov, V. I. Pavlov×
Obukhov Institute of Atmospheric Physics of the PAS, 109017 Moscow, Russia
×UFR de Mathématiques Pures et Appliquées, Universitéde Lille 1, 59655 Villeneuve d'Ascq, France
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 (t0-t)γ, where t0 is the collapse
time, with γ=-1,-2, and γ=-2/3,-1 for the isotropic and
anisotropic collapses, respectively. The rigorous criterion of collapse is found on
the base of integrals of motion.