HIGHLY NONLINEAR-INTERACTIONS BETWEEN A GRAVITY-WAVE AND A CURRENT OF CONSTANT VORTICITY

Abstract

The Fourier series method is employed to calculate particle velocity, wavelength and wave profile of a gravity wave propagating on a vertically varying linear shear current. From the comparisons between predicted values and experimental data, it is found that highly nonlinear interaction resulting from a shear current has significant effects on the wave field, and that the lower order wave theories give poor prediction. For waves of the same height and period, the shear current causes a change in wavelength and wave profile. An adverse shear current shortens wavelength; contrarily wavelength is enlarged by a favourable current. The wave crest is steepened and the trough becomes flat when the wave and favourable shear current are moving in the same direction. The wave surface profile becomes more asymmetrical about the mean water level when a favourable current exists.