International Conference «Mathematical and Informational Technologies, MIT-2013»
(X Conference «Computational and Informational Technologies for Science,
Engineering and Education»)

Vrnjacka Banja, Serbia, September, 5–8, 2013

Budva, Montenegro, September, 9-14, 2013

Fedotova Z.I.   Khakimzyanov G.S.  

Nonlinear-dispersive models on a rotating sphere: the new derivation and conservation laws

Reporter: 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
sphere // J. Appl. Mech. Tech. Phys.  2011. Vol. 52, № 6. P. 865-876.
2. Fedotova Z.I.,  Khakimzyanov G.S.  An derivation analysis of nonlinear dispersive equations // Comp. technology. 2012. Vol. 17, № 5. P. 94-108.

Abstracts file: Abstract-MIT.rtf
Full text file: Paper-MIT-2013.pdf

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