Wave Breaking Dissipation in the Wave-Driven Ocean Circulation

Abstract

If wave breaking modifies the Lagrangian fluid paths by inducing an uncertainty in the orbit itself and this uncertainty on wave motion time scales is observable as additive noise, it is shown that within the context of a wave?current interaction model for basin- and shelf-scale motions it persists on long time scales. The model of McWilliams et al. provides the general framework for the dynamics of wave?current interactions. In addition to the deterministic part, the vortex force, which couples the total flow vorticity to the residual flow due to the waves, will have a part that is associated with the dissipative mechanism. At the same time the wave field will experience dissipation, and tracer advection is affected by the appearance of a dissipative term in the Stokes drift velocity. Consistency leads to other dynamic consequences: the boundary conditions are modified to take into account the diffusive process and proper mass/momentum balances at the surface of the ocean. In addition to formulating how a wave?current interaction model is modified by the presence of short-time events that induce dissipation, this study proposes a stochastic parameterization of dissipation. Its relation to other alternative parameterizations is given. Two focal reasons make stochastic parameterizations attractive: one can draw from extensive practical modeling experience in other fields, and it ties in a very natural way to a wealth of observational data via statistics.