Predicting turbulence in flows with strong stable stratification

High resolution direct numerical simulations are used to understand how turbulence can be predicted in flows subject to strong stable stratification. It is observed that shear instabilities are the predominant cause of turbulence in the simulations, which supports the derivation of a Froude-Reynolds number scaling to predict turbulence in this flow regime. It is found that when the autocorrelation length of the horizontal velocities is used as the length scale for the Froude and Reynolds number then that length scale, the Froude number, and the Reynolds number all evolve, as theory suggests. An advection length scale based on the kinetic energy and its dissipation rate is found not to be of practical use for characterizing the flow. Finally, it is observed the Froude-Reynolds number parameter of Riley and de Bruyn Kops is very similar to the commonly used buoyancy Reynolds number. This suggests that a shear-based approach to parametrizing turbulence under stable stratification, rather than the ratio-of-length-scales approach that is often used as the physical justification for the buoyancy Reynolds number, might be appropriate. While the Froude-Reynolds parameter and the buoyancy Reynolds number are closely related, the former may be the more useful when configuring laboratory experiments or numerical simulations since it can be estimated a priori.