I.T.Selezov Propagation of nonlinear transient surface gravity waves over uneven botton |
Applied hydromechanics, Vol. 1 (73) ¹ 1, (1999) |
| Some mathematical models of wave hydrodynamics of the shelf zone are presented. Corresponding numerical solutions demonstrating new characteristic effects of the interaction of nonlinear water waves with a bottom relief are obtained. The exact 2-D statement includes the Lapace equation for velocity potential, the nonlinear conditions on the free surface and the conditions on a bottom surface. On this basis nonlinear-dispersive asymptotic approximations describing wave propagation over a bottom relief are obtained. At that, it is assumed that the dispersion parameter b and the boottom surface gradient g are small, while the nonlinear parameter a is arbitrary value unlike widely spreading traditional approximate theories. Also, a nonlinear model to investigate a movement of salt sea water, as well as a bottom reforming due to waves propagating over an uneven bottom are presented. Corresponding initial-boundary value problem is solved by a finite-difference method for given multiincident wave pulses of the semi-sine form generated at inlet. Moreover, the similar problem is considered on the basis of KdV equation when solitons are given at inlet. The results of numerical calculations and their analysis are presented. |
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| TEXT LANGUAGE: Russian |