An Improvement to Stokes Nonlinear Theory for Steady Waves

Abstract

An improvement to Stokes nonlinear theory for steady water waves is presented. The method is based on the solution of the kinematic and the dynamic free-surface boundary conditions. The expression of the stream function is taken from the Stokes V theory. The numerical method is a very simple iterative procedure. The method is valid at any depth greater than U=HL2/d3= 40, where U is the Ursell number, L is the wavelength, d is the mean depth, and H is the wave height. The error in the free-surface boundary conditions is relatively small. The proposed solution is validated against Stokes V theory, a stream function theory, and experimental data as far as the surface elevation and horizontal velocity distribution are concerned. For high waves, near breaking limit, the method gives better results in comparison with Stokes V theory.