Stokes Theory for Waves on Linear Shear Current

Abstract

A third‐order Stokes theory for waves on a linear shear current is outlined. Pressure predictions from the theory must recognize a vorticity term in the Bernoulli equation. Solutions may use either of the Stokes definitions of wave speed. Using the Stokes first definition, comparative predictions are presented for wave number, crest elevation, horizontal velocity, horizontal acceleration, dynamic pressure, mean energy level, and the Stokes drift. Predictions of parameter dependence on dimensionless wave height, dimensionless water depth, dimensionless mean current, and dimensionless vorticity indicate that vorticity at realistic levels is unimportant and that height, depth, and current remain the dominant influences.