Models of turbulence in the marine environment —a comparative study of two-equation turbulence models

This study compares the performance of the most widely used two-equation turbulence closures for marine and atmospheric applications, the k– and the Mellor–Yamada level 2.5 (MY) model. For a better understanding, the physical equations are given in a joint notation. Stability functions originally suggested by Galperin et al. (1988) are used here with slight modifications in order to allow for numerically stable computations of free convection. For the k– models, a flux boundary condition for the dissipation rate is tested. In contrast to the classical Dirichlet condition, its straightforward discretization allows for sufficient accuracy also in three-dimensional models with coarse vertical resolution. The models are then applied to idealized situations including free convection, wind mixing and stratified steady-state boundary layer flow. Finally, the spring development of thermal surface stratification as measured during the FLEXʹ76 experiment is simulated. For all these different, partially complex situations, the k– and the MY model proved to perform similarly.