Numerical Models with Reynolds Equation Based Energy Dissipation for Plunging Breakers on a Uniform Slope

Abstract

Practical two-dimensional numerical models investigating the internal characteristics of plunging breakers on a uniform slope are proposed under the assumption that the energy dissipation associated with the turbulence and vortex motions after wave breaking can be evaluated directly by the Reynolds stress terms. In these models, the Reynolds stress terms are expressed using Prandtl's mixing length model. The energy dissipation is evaluated using internal kinematic quantities (vorticity and shear distortion rate) because laboratory experiments have revealed that the energy dissipation of plunging breakers demonstrate a strong correlation to internal kinematic quantities. A new concept termed “vortex radius” is defined as the circulation divided by the local horizontal velocity, and the representative scale of length is given by this vortex radius. Even though the representative scale of length is evaluated using the zero-order turbulence model, the scale changes spatially in accordance with flow conditions. The qualitative and quantitative accuracies of the models are examined by comparing turbulence properties with experimental results for plunging breakers on a uniform slope. Furthermore, the internal characteristics of plunging breakers are numerically investigated.