The transfer of momentum from waves to currents due to wave breaking

Abstract

The research presented in this dissertation focuses on understanding the dynamics of waves and currents in the presence of wave breaking. The simplest approach, direct numerical simulation of the ocean dynamics, is computationally prohibitive–waves typically have periods of tens of seconds, while currents vary on times from hours to days. This work uses a multi-scale asymptotic theory for the waves and currents (Craik and Leibovich, 1976; McWilliams et al., 2004), similar to Reynolds-averaged Navier-Stokes, in order to avoid resolving the wave field. The theory decomposes the total flow into the mean flow (current) and fluctuations (waves), then takes a moving time average of the total flow equations to determine the wave forcing on the current. The main challenge is extending this theory to include a physical model for dissipative wave effects, notably breaking, in terms of the wave age, wind speed, and bottom topography. Wave breaking is difficult to observe, model, and predict, because it is an unsteady, non-linear process that takes place over disparate scales in both space and time. In the open ocean, white-capping often covers less than 2% of the surface, yet still plays an important role in the flux of mass, momentum, heat, and chemicals between the atmosphere and ocean. The first part of this dissertation proposes a stochastic model for white-capping events, and examines the stability of the ensemble average of these events. Near the shore, the decreasing ocean depth causes waves to overturn and break. Over time, this drives currents that erode sediment from beaches and deposit it around coastal structures. These currents are often so strong that their effect on the wave field, and thus their own forcing, is significant. A detailed analysis of this phenomena makes up the second part of this dissertation.