Numerical Simulation of Nonlinear Surface Gravity Waves Transformation under Shallow-Water Conditions

Abstract

This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.

Transformation of Nonlinear Surface Gravity Waves under Shallow-Water Conditions

“…In the first approximation, solution of Equation (1) consists of primary waves and takes the form [10]:…”

“…In work [10] discussed the problem of nonlinear surface waves propagation under shallow-water conditions. Shallow-water equation taking account of quadratic nonlinearity was solved by the method of successive approximations.…”

“…There was an attempt to describe not only the initial wave crest sharp-ening but further steepening of its leading edge. One uses rather understandable and vivid semigraphical method based on energy conservation law given in [10].…”

Study of Dissipating of Wave Energy in the Breakers Zone of the Gulf of Guinea: Case of Autonomous Port of Cotonou in Benin Coastal Zone

“…Benin coast is more or less linear and cut off in two places, namely, the Bouche du Roy and the channel mouth of Cotonou. Its coastal zone is between latitude 6˚15' and 6˚23' north [7].…”

“…), we obtain the following [15]: = a g (7) By approximating the direction of swell spread to a straight line, the wave's position r and its velocity v are specified on the mark ( )…”