NONLINEAR –DISPERSIVE MODELS ON A ROTATING SPHERE:THE NEW DERIVATION AND CONSERVATIVE LAWS.
Z. I. Fedotova and G. S. Khakhimzyanov
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 direction of depth of the liquid layer.
In [1], 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 that the NLD-equations 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 under the assumption of 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, the use of technology scaling basic hydrodynamic quantities and introducing the small parameters allowed to obtained a class of simplified  NLD-equations for which the main characteristics of the original model (there is a balance of both kinetic and total energy) are preserved.
This work was supported by the Russian Foundation for Basic Research (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. (Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 52, No. 6, pp. 22–35.
2. Fedotova Z.I,  Khakimzyanov G.S.  An derivation analysis of nonlinear dispersive equations // Comp. technology. 2012. Vol. 17, № 5. P. 94-108.