A perturbative theory of the evolution of the center of typhoons. (English) Zbl 1169.86307

Dobrokhotov, Sergey; Semenov, Evgeny; Tirozzi, Brunello

Aoki, Takashi (ed.) et al., Zeta functions, topology and quantum physics. Papers of the symposium, Osaka, Japan, March 3–6, 2003. New York, NY: Springer (ISBN 0-387-24972-9/hbk; 0-387-24981-8/e-book). Developments in Mathematics 14, 31-50 (2005).

Summary: We develop the theory of quasi linear systems of PDE introduced by V. P. Maslov. According to this theory many 2-D quasi linear systems of PDE possess only three algebras of singular solutions with properties of “structural” self-similarity and stability. They are the algebras of shock waves, “narrow” solitons and “square root” point singularities (solitary vortices). Their propagation is described by an infinite chain of ODE (the Hugoniót-Maslov chains)obtained by a Taylor expansion of the solution of the shallow water equation around the point of the singularity. We consider the case of the “square root” singularity and connect it with the description of typhoons. We show the connection of this theory with the evolution of the center of typhoons.
For the entire collection see [Zbl 1082.11001].

MSC:

86A10	Meteorology and atmospheric physics
35L60	First-order nonlinear hyperbolic equations
35L65	Hyperbolic conservation laws
35L67	Shocks and singularities for hyperbolic equations
76B47	Vortex flows for incompressible inviscid fluids