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 |