Vorticity–Stream Function Formulation for Turbulent Oscillatory Boundary Layer over the Sea Bottom

Abstract

The oscillatory flow within the oscillatory boundary layer at the bottom of propagating surface waves is determined by numerically solving the vorticity–stream function problem when the flow regime is turbulent. Two alternative vorticity equations are considered. The first equation is “exact” and is obtained by applying the curl operator to the Reynolds equation. The second equation is obtained by assuming that a turbulent eddy diffusivity is linearly related to the turbulent eddy viscosity and can be used to model the vorticity dynamics close to the bottom. Even though the second equation requires less computational resources and has been employed previously, it provides inaccurate results, and the use of the full equation is recommended.