Vertical variations of wave-induced radiation stress tensor

The distributions of the wave-induced radiation stress tensor over depth are studied by using the linear wave theory, which are divided into three regions, i.e., above the mean water level, below the wave trough level, and between these two levels. The computational expressions of the wave-induced radiation stress tensor at the arbitrary wave angle are established by means of the Eulerian coordinate transformation, and the asymptotic forms for deep and shallow water are also presented. The vertical variations of a 30° incident wave-induced radiation stress tensor in deep water, intermediate water and shallow water are calculated respectively. The following conclusions are obtained from computations.The wave-induced radiation stress tensor below the wave trough level is induced by the water wave particle velocities only, whereas both the water wave particle velocities and the wave pressure contribute to the tensor above the wave trough level. The vertical variations of the wave-induced radiation stress tensor are influenced substantially by the velocity component in the direction of wave propagation. The distributions of the wave-induced radiation stress tensor over depth are nonuniform and the proportion of the tensor below the wave trough level becomes considerable in the shallow water. From the water surface to the seabed, the reversed variations occur for the predominant tensor components.