On the Depth of Wave Influence

Abstract

Two physical ideas are combined to derive an expression for the depth of wave influence of a surface gravity wave without assuming the fluid motion is irrotational. One idea is that in the reference frame which makes the wave steady, the static pressure difference between crest and trough balances the dynamic pressure difference between crest and trough. The other idea is that at the depth of wave influence, the pressure under the crest equals the pressure under the trough due to the vertical acceleration of the fluid being downward at the crest and upward at the trough. The depth of wave influence is directly proportional to the wave length and independent of the wave height if the wave height is small compared to the wave length.