PRESSURE AND SET DOWN FOR HIGHER-ORDER STOKES WAVES ON CURRENT

The Bernoulli equation for higher-order Stokes waves on a steady curre nt over a horizontal, impermeable bed was analyzed, and an ambiguity w as detected in the determination of the wave-induced pressure at even- order theories. This leads to the introduction of a new (reduced) Bern oulli constant. A simple relation between this quantity and the curren t-wave set down is presented, and the set down correct to the fourth o rder 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. Fi nally, the difference between a wave quantity belonging to nth-order t heory and being correct to the nth order is discussed, and guidelines are offered for the determination of the former and the corresponding dispersion relation.