Second-order turbulence closure models for geophysical boundary layers. A review of recent work

Recent contributions to second-order turbulence modelling are reviewed with an emphasis on models of the coastal ocean. Classical and recent turbulence models are reformulated using a unifying notation, making differences in model structure and model parameters more transparent. The essential characteristics of a number of models are compared. It is further demonstrated that the mathematical stability and realisability of the models is crucial for practical applications. The parameter constraints to insure stable computations are discussed. Model performance is evaluated for a number of idealised entrainment scenarios that are typical for shelf seas: entrainment in linearly stratified and two-layer fluids caused by (a) surface wind stress (b) bottom stress due to water motion driven by a barotropic pressure gradient (c) bottom stress due to water motion in a bottom jet. It is shown that the predicted entrainment velocities are in good agreement with available laboratory data, provided the models have been calibrated according to a theoretical constraint. In addition, model behaviour in free convection is re-analysed with the help of recent data from large eddy simulations (LES). It is shown that even the most simple models, which do not solve a differential equation for the turbulent kinetic energy (TKE), can approximately reproduce the entrainment depth, however, they fail completely in reproducing the correct budget of the TKE-balance. In contrast, second-order models solving transport equations for the TKE and a length scale determining variable are in reasonable agreement with the TKE-budgets from LES.