Propagation of nonlinear transient surface gravity waves over uneven bottom (Q2711674)

First, some mathematical models of wave hydrodynamics of the shelf zone are discussed. Then a two-dimensional problem is stated for Laplace equation including nonlinear conditions on the free surface and conditions on the bottom surface. On this basis, nonlinear-dispersive asymptotic approximations describing wave propagation over a bottom relief are derived. At that, it is assumed that the dispersion parameter \(\beta\) and the boottom surface gradient \(\gamma\) are small, while the nonlinear parameter \(\alpha\) is an arbitrary value unlike widely used traditional approximate theories. For this model the initial-boundary value problem is stated and solved by a finite difference method.NEWLINENEWLINE Another nonlinear problems for the motion of salt sea water and the bottom reforming due to waves propagating over an uneven bottom are presented. The corresponding initial-boundary value problem is solved by a finite difference method for multiple wave pulses of semi-sine form. Moreover, the similar problem is considered on the basis of KdV equation for soliton pulse propagation. The results of numerical calculations are presented.