Authors : Alpha Malick Ndiaye; Fadel Diop; Ibrahima Kama; Cheikh Mbow

Volume/Issue : Volume 11 - 2026, Issue 1 - January

Google Scholar : https://tinyurl.com/2cnxt32r

Scribd : https://tinyurl.com/58p4zcp3

DOI : https://doi.org/10.38124/ijisrt/26jan338

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Abstract : The movement of currents and water particles in the oceans, both at the surface and at depth, plays an important role in ocean circulation and the description of surface waves. The movement of water particles is generally influenced by the passage of surface waves. This movement provides a better understanding of the influence of waves on the movements of water particles at the surface and at the bottom. In this study, the evolution of wave and particles movement can be determined by considering a channel with linearly varying bottom. The nonlinear Stokes theory equations to be solved in this case will allow us to determine the solutions for the hydrodynamic wave parameters. Because of the non-linearity of the equations, finite difference method and iterative method of Gauss-Siedel by using the Successive over relaxation (S.O.R.) are used to resolve numerically the nonlinear equations. Our results are obtained using the FORTRAN and MATLAB software to visualize the temporal propagation of the wave in the channel and its influence on the water motion at the free surface and at the bottom. Finally, we will also look at the influence of the linear bottom on the evolution of the wave and the movement of water particles.

Keywords : Surface Waves, Channel, Movement of Water Particles, Nonlinear Equations, Finite Difference Method.

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