Phase velocity and dispersion relations of surface gravity waves in shallow sea

Abstract

Phase velocity and dispersion relations of surface gravity waves on the sea have been modelled by two numerical methods and the results compared with previous experimental studies. Wave nonlinearities cause deviations from linear wave relations and these deviations are seen on the sea surface in the form of sharply crested waves. The effects are amplified if wave steepness increases or wave spectra become narrower. When the effects of finite depth of water are included in the calculations, the deviations from linearity are found to increase significantly.