International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)
Fedotova Z.I. Khakimzyanov G.S.Nonlinear-dispersive models on a rotating sphere: the new derivation and conservation lawsReporter: Fedotova Z.I.Our purpose is to further improve and study of mathematical models used to simulate the long-wave processes in the ocean, which do not require a detailed description of the flow structure in the depth direction. In [1], the nonlinear-dispersive (NLD) model on the sphere has been obtained with using the potential flow conditions. In [2], for the case of plane geometry it has been shown they can be obtained under replacing the potentiality condition by the new condition, that is: the `` main'' part of horizontal velocity component is independent from ``vertical'' position, which is natural for long-wave nature flow. In the present paper, a similar result was obtained in a spherical geometry taking into account the mobility of the bottom surface. In addition a class of simplified NLD-equations was derived for which the balance of both kinetic and total energy is preserved. This work was supported by the RFBR (12-01-00721-a), and the program of the State Support of Scientific Schools of the Russian Federation (6293.2012.9).
1. Fedotova Z.I., Khakimzyanov G.S. Full nonlinear dispersion model of shallow water equations on a rotating
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