Simulating interaction of nonlinear spatial waves on a free surface of the shallow viscous liquid layer

This paper deals with the combined approach to describing the evolution of weakly nonlinear three-dimensional moderately long perturbations of free surface of viscous liquid. The initial system of hydrodynamic equations is reduced to the novel model system of equations. The first of them is integro-differential equation for nonlinear perturbation of the free surface, taking into account non-stationary shear stress on a weakly sloping bottom. Another equation is an auxiliary linear equation for determining the liquid horizontal velocity vector, averaged over the layer depth. This vector is present in the main equation only in the term of the second order of smallness. The proposed model is suitable for finite-amplitude waves, traveling in different directions in the horizontal plane. Some problems of interactions and collisions of such perturbations over the horizontal and weakly sloping bottom are solved numerically.