The performance of subgrid-scale models in large-eddy simulation of Langmuir circulation in shallow water with the finite volume method

Langmuir turbulence consists of Langmuir circulation (LC) generated at the surface of rivers, lakes, bays, and oceans by the interaction between the wind-driven shear and surface gravity waves. In homogeneous shallow water, LC can extend to the bottom of the water column and interact with the bottom boundary layer. Large-eddy simulation (LES) of LC in shallow water was performed with the finite volume method and various forms of subgrid-scale (SGS) model characterized by different near-wall treatments of the SGS eddy viscosity. The wave forcing relative to wind forcing in the LES was set following the field measurements of full-depth LC during the presence of LC engulfing a water column 15 m in depth in the coastal ocean, reported in the literature. It is found that the SGS model can greatly impact the structure of LC in the lower half of the water column. Results are evaluated in terms of (1) the Langmuir turbulence velocity statistics and (2) the lateral (crosswind) length scale and overall cell structure of LC. LES with an eddy viscosity with velocity scale in terms of $S$ and $\Omega$ (where $S$ is the norm of the strain rate tensor and $\Omega$ is the norm of the vorticity tensor) and a Van Driest wall damping function (referred to as the S-Omega model) is found to provide best agreement with pseudo-spectral LES in terms of the lateral length scale and overall cell structure of LC. Two other SGS models, namely the dynamic Smagorinsky model and the wall-adapting local-eddy viscosity model are found to provide less agreement with pseudo-spectral LES, for example, as they lead to less coherent bottom convergence of the cells and weaker associated upward transport of slow downwind moving fluid. Finally, LES with the S-Omega SGS model is also found to lead to good agreement with physical measurements of LC in the coastal ocean in terms of Langmuir turbulence decay during periods of surface heating.