On the effects of wave steepness on higher order Stokes waves

Abstract

The effect of wave steepness on higher order finite amplitude Stokes waves is investigated analytically and numerically. It is shown that the phase speed increases as the wave steepness increases thereby initiating the wave instabilities. As the order increases, the phase speed also increases .However, the impact of wave steepness on phase speed is more pronounced for the wave steepness parameter ε𕟲.09 where 0.02 ≥ ┒ ≥ 0.33 Beyond the upper bound, instability – wave breaking comes in. JONAMP Vol. 11 2007: pp. 369-374