Modeling rotating flows with neutral and unstable stratification

Abstract

We investigate the effect of rotation on the structure of turbulence in neutral and convective mixed layers and assess the applicability of the Reynolds stress turbulence closure models to studies of deep convection. Unlike in the case of stable stratification, where rotational contribution is limited (Galperin et al., 1989), in neutral and convective flows this contribution is significant. The rotational terms endow eddy viscosity and eddy diffusivity with tensorial properties and algebraic complexity. In the present study we thoroughly investigate the mathematical features of this tensorial eddy viscosity‐eddy diffusivity formulation. To ensure physical readability of the model, we found it necessary to impose upper bounds on the dimensionless velocity and temperature gradients in the expressions for eddy coefficients. It was also found absolutely crucial to include in the model a limitation on the magnitude of the turbulence macroscale due to background rotation. This limitation is similar to the one imposed by stable stratification. The self‐similar solutions derived from the model are compared with the experimental data by Fernando et al. (1991) and are shown to be in good agreement. Implications of the results for oceanographic modeling and for simulation of deep convection are discussed.