Institute of Computational Mathematics and Mathematical Geophysics SB RAS

International Conference on Mathematical Methods in Geophysics «MMG-2008»

Akademgorodok, Novosibirsk, Russia, October 13-15, 2008

Abstracts

Mathematical and Statistical Simulation in Problems of the Physics of Atmosphere, Ocean, and Environmental Protection

Exact solutions of the rotating shallow water equations

Chesnokov A.

Lavrentyev Institute of Hydrodynamics (Novosibirsk)

The rotating shallow water theory is widely-used nonlinear approximation for atmospheric and oceanic motions in the midlatitudes with relatively large length and time scales. This theory applies to phenomena that do not depend substantially on temporal changes of the density stratification. The model is a system of nonlinear partial differential equations which are difficult to solve analytically. In this work the Lie symmetries of the rotating shallow water equations are investigated, the replacement of variables that transform the shallow water model to the rotating shallow water equations is obtain. New classes of the exact solutions to the model, including time-periodical solutions, are presented with a brief physical interpretation.

Note. Abstracts are published in author's edition

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