Turbulent viscosity in natural surf zones

Abstract

Waves breaking in the shallow surf zone near the shoreline inject turbulence into the water column that may reach the bed to suspend sediment. Breaking-wave turbulence in the surf zone is, however, poorly understood, which is one of the reasons why many process-based coastal-evolution models predict coastal change during severe storms inadequately. Here, we use data collected in two natural surf zones to derive a new parameterization for the stability function Cm that determines the magnitude of the eddy viscosity nt in two-equation turbulent-viscosity models, nt = Cmk2/ɛ, where k is turbulent kinetic energy and ɛ is the turbulence dissipation rate. In both data sets, the ratio of turbulence production to dissipation is small (≈0.15), while vertical turbulence diffusion is significant. This differs from assumptions underlying existing Cm parameterizations, which we show to severely overpredict observed Cm for most conditions. Additionally, we rewrite our new Cm parameterization into a formulation that accurately reproduces our Reynoldsstress based estimates of turbulence production. This formulation is linear with strain, consistent with earlier theoritical work for large strain rates. Also, it does not depend on ɛ and can, therefore, also be applied in one-equation turbulentviscosity models. We anticipate our work to improve turbulence modeling in natural surf zones and to eventually lead to more reliable predictions of coastal evolution in response to severe storms.