Effects of Wave Breaking on the Near-Surface Profiles of Velocity and Turbulent Kinetic Energy

Abstract

A theoretical model for the near-surface velocity profile in the presence of breaking waves is presented. Momentum is accumulated by growing waves and is released upon wave breaking. In effect, such a transition is a process involving a time-dependent surface stress acting on the mean current. In this paper, conventional theory for the Stokes drift is expanded to fourth-order accuracy in wave steepness. It is shown that the higher-order terms lead to an enhancement of the surface Stokes drift and a slight retardation of the Stokes volume flux. Furthermore, the results from the wave theory are used to obtain a bulk parameterization of momentum exchange during the process of wave breaking. The mean currents are then obtained by application of a variation of the ?level 2.5? turbulence closure theory of Mellor and Yamada. When compared with the traditional approach of a constant surface stress, the mean Eulerian current exhibits a weak enhancement in the near-surface region, compensated by a negative shift deeper in the water column. However, it is found that the results of Craig and Banner and the results of Craig are not significantly affected by the present theory. Hence, this study helps to explain why the Craig and Banner model agrees well with observations when a realistic, time-varying surface stress acts on the drift currents.