Pressure and Set Down for Higher‐Order Stokes Waves on Current

Abstract

The Bernoulli equation for higher‐order Stokes waves on a steady current over a horizontal, impermeable bed was analyzed, and an ambiguity was detected in the determination of the wave‐induced pressure at even‐order theories. This leads to the introduction of a new (reduced) Bernoulli constant. A simple relation between this quantity and the current‐wave set down is presented, and the set down correct to the fourth order in wave steepness is calculated. The finding of the fourth‐order current‐wave set down is a necessary step to allow calculation of the wave height for fourth‐order shoaling in the presence of a current. Finally, the difference between a wave quantity belonging to