Analysis of Stokes waves theory as a diffusion problem

Abstract

This mathematical model concerns the theory of Stokes waves. These wave types belong to the class of ocean surface waves found in deep and intermediate waters. In this consideration, the fifth order expansion was obtained using Korteweg de Vries equation with diffusion term. This study suggests that the phase velocity grows with increase in wave steepness whilst the group velocity shows the opposite tendency .The effect of diffusion introduced through depth distribution is obvious as the solutions apparently depend strongly on the water depth in inverse form. Interestingly, this analysis strongly suggests that the peak for potential energy lies between second and third order solutions while that of kinetic energy attains the peak at second and then becomes fairly stable. High seismic response associated with sea-bed motion corresponding to second order solution strongly support the result. However, the effect of additional terms on the wave profile appears somewhat insignificant. The wave profile of first order to fifth order in this consideration remains unchanged as expected.

Journal of the Nigerian Association of Mathematical Physics Vol. 10 2006: pp. 59-68