Simulating the Wave-Enhanced Layer under Breaking Surface Waves with Two-Equation Turbulence Models

Abstract

The purpose of this paper is to modify two-equation turbulence models such that they are capable of simulating dynamics in the wave-enhanced layer near the surface. A balance of diffusion of turbulent kinetic energy (TKE) and dissipation is assumed as the surface boundary condition for TKE following the suggestion of Craig and Banner. It is shown that this theory, originally developed under the assumption of a macro length scale linearly increasing down from the surface, fails for two-equation models such as the well-known k?ε model. Suggestions are made how to modify such models for overcoming this deficiency. The basic idea is to insert the analytic solution of a model problem suggested by Craig into the dissipation rate equation and solve for the turbulent Schmidt number of the dissipation rate equation, which may be formulated as a function of the production/dissipation ratio. With this modification, the linear behavior of the macro length scale is properly reproduced by the k?ε model. It is shown how near-surface dissipation rate measurements under breaking waves can be simulated by an extended k?ε model considering a shear-dependent closure for the second moments. Finally, the overall performance of this new model approach is tested with a typical upper mixed layer scenario in the northern North Sea.