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A mathematical model for hurricanes. (Un modèle mathématique de cyclone.) (French) Zbl 1171.76457
Summary: Source waves are particular solutions to genuinely nonlinear hyperbolic systems with a source term, whose propagation velocity is a constant determined by the roots of this source term. We propose a system of two equations on a two-dimensional space, which models the velocity field of the atmosphere near the ground. The source term is made of three parts: a given pressure gradient, a friction or aspiration effect and the Coriolis force. In the case where these parameters are constant, we build a solution which is a constant outside a circular crown. The internal circle represents the wall of the eye of the hurricane and corresponds to a share shock wave. The external circle is a set generating the bifurcation which actually models the hurricane.
MSC:
76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics
86A10 Meteorology and atmospheric physics
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