Further on stokes expansions for the finite amplitude water waves

Abstract

An analytic method is applied to study the higher order approximate solution of Stokes waves. For comparison and effective analysis, solutions of first to fifth order approximations are studied. From the various expressions derived, the numerical computations and the graphical solutions, there is a gradual increase in the wave height from the first to fifth order and they follow one another very closely. However, there is a significant difference in that of fourth and fifth order compared with those of first to third. This analysis suggests that the wave height of fifth order is twice that of third order but with slight increase with respect to the fourth order solution. Fifth order Stokes waves may be peculiar to waves with unusual characters in view of the significant difference in the wave height when compared with those of lower order solution. However, dispersive phenomena among wave modes often limit the wave growth in practice. Journal of the Nigerian Association of Mathematical Physics Vol. 8 2004: pp. 227-236