Vertical variation in radiation stress and wave-induced current

Abstract

In this paper, the traditional concept of radiation stress in water waves is extended to its vertical profile in a new technical way. The definition of and calculation formulae for the vertical profile of radiation stress are advanced. The wave-induced currents over a slopping bottom are modeled. In the simulated example, the wave set-up and set-down, and the vertical structure of wave-induced currents inside and outside the surf zone are successfully modeled. The modeled wave set-up and set-down agree well with the analytical results. The model results reveal also two wave-induced vertical circulations with opposite directions; and the flow pattern agrees well with the measurement of a laboratory experiment. The application of radiation stress with vertical variation is expected to play an important role in the studies of near-shore current systems.