Abstracts

The combined method for the dynamics description of nonlinear three-dimensional perturbations of the shallow liquid layer free surface, which propagated simultaneously under the different angles, was proposed by authors previously [1]. In this paper the approach is applied for two-layered fluid bounded not only by a gently sloping bottom, but also by a lid.

The initial system of the equations of motion and the continuity equations in layers of viscous incompressible immiscible liquids is reduced to one principal evolution equation for the interface disturbance and two elementary auxiliary equations, which are necessary for a determination of the fluids horizontal velocity vectors, averaged over the depths of the layers and contained in the main equation only in the terms of the second order of smallness. All the coefficients in this equation are depended only on the geometrical and on the physical parameters of the problem [2]. The suggested model is suitable for weakly nonlinear waves running simultaneously in various horizontal directions. Some solutions of this system of equations were found numerically.

This work is supported by the RFBR ( grant No. 07-01-00574 ).

References:

1. Arkhipov D.G., Khabakhpashev G.A. New approach to the description of spatial nonlinear %waves in dispersive media // Dokl. Phys. 2006. V. 51. No 8. P. 418-422.

2. Khabakhpashev G.A. Transformation of long nonlinear waves in a two-layer viscous fluid between a gently sloping lid and bottom // J. Appl. Mech. Tech. Phys. 2005. V. 46. No 6. P. 807-817.

Note. Abstracts are published in author's edition

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