An Improved Second-Moment Closure Model for Langmuir Turbulence Conditions: Model Derivation and Validation

Abstract

In this study, an improved second-moment closure model, the so-called k-ω model, which takes into consideration the Langmuir turbulent effect in the transport equations of turbulent kinetic energy and turbulent frequency, was developed. The Langmuir turbulent effect was also included in the vertical eddy viscosity and diffusivity coefficient. Langmuir turbulence production, as well as buoyancy production, anisotropic production, and vorticity production induced by velocity shear, was included in the pressure covariance parameterization to derive the stability function. The Langmuir effect and relatively complete pressure covariance parameterization inclusion can account for the influences of Langmuir turbulence and stratification in the vertical eddy viscosity and vertical eddy diffusion coefficients. Based on the modified model, one-dimensional numerical experiments for horizontally homogeneous flows were carried out. The results indicate that the modified model is more accurate than other models in terms of the vertical eddy viscosity, vertical turbulence velocity variance, kinetic energy, and mean velocity profile compared with the large eddy simulation results. The simulated sea surface temperature (SST) and mixed layer depth of the modified model were compared with observations at Ocean Station Papa. When considering Langmuir turbulent effects, the modified model overcomes the shortcoming that the simulated SST is higher than the observed SST. Numerical results indicate that the k-ω model performs better than the k-kl model, although both models consider the Langmuir turbulent effect in the simulation of upper mixing motions.