Institute of Computational Mathematics and Mathematical Geophysics

Abstracts

Mathematical modeling of processes in atmosphere and hydrosphere

This paper deals with the development of the weakly nonlinear theory describing the transformation of the three-dimensional free boundary disturbances of an ideal incompressible fluid [1]. Using the previous suppositions [2], the initial hydrodynamic equations (equations of continuity and motion) were reduced to the one equation for three-dimensional perturbations of the two-layer liquid interface over a gently sloping bathymetry.

Now to determine the displacements of the free surface it was assumed that lengths of the internal waves are significantly greater than the depth of the upper layer. As a result, it was deduced the evolution equation from which disturbances of the free surface can be determined with the help of a solution previously obtained for the interfacial waves.

Some solutions of this model evolution equation were found numerically using the method described in the paper [3]. In particular it was considered a superposition at the free surface of the progressive harmonic oscillation and the disturbance induced by the running solitary ondulatory interfacial wave propagating over the gently sloping bottom. It is observed both intensification and decreasing of the oscillations on the back front of the wave. It is like to the interference of the free surface oscillations and the perturbation induced by the solitary internal wave.

References:

[1] G.A. Khabakhpashev, Izvestija, Atm. Oceanic Phys., 1996, V. 32, No. 6, P. 773-778.
[2] G.A. Khabakhpashev, Izvestija, Atm. Oceanic Phys., 2001, V. 37, No. 3, P. 368-377.
[3] G.A. Khabakhpashev, A.A. Litvinenko, {it Proc. Int. Conf. Comput. Math.}, Pt 2, Novosibirsk, Inst. Comput. Math. Math. Geophys., 2002, P. 518-523.

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