Radiation stresses in water waves; a physical discussion, with applications

Abstract The radiation stresses in water waves play an important role in a variety of oceanographic phenomena, for example in the change in mean sea level due to storm waves (wave “set-up”); the generation of “surf-beats”; the interaction of waves with steady currents; and the steepening of short gravity waves on the crests of longer waves. In previous papers these effects have been discussed rigorously by detailed perturbation analysis. In the present paper a simplified exposition is given of the radiation stresses and some of their consequencies. Physical reasoning, though less rigorous, is used wherever possible. The influence of capillarity on the radiation stresses is fully described for the first time.