Turbulence budgets in shearless, inhomogeneous, and stably stratified turbulence*

Large scale simulations of the Earth’s oceans and atmosphere rely on crude parameterizations of turbulent processes using bulk quantities due to the prohibitive mesh resolution required to capture these processes directly. An interesting flow regime useful for evaluating existing models is one in which shearless turbulence, generated in a localized region of space, decays and interacts with background stratification, a scenario common in geophysical settings.

 

We conducted a series of high-resolution large eddy simulations to investigate this problem. As is typical in problems of stable stratification, internal gravity waves become a confounding influence in the data when computing turbulence statistics. While the waves are a key dynamical component of the system, they do not contribute to turbulent mixing and therefore complicate efforts to derive reliable parameterizations. We developed a filtering procedure based on the linear eigen-modes of the base state density profile. Significant improvement in turbulence quantities resulted when projecting out the linear eigen-modes, which constitute more than 30% of the kinetic energy in certain regions. We apply this projection procedure to the budget equations for vertical and horizontal TKE, buoyancy variance, and density flux, giving a clearer path forward to developing models of the mixing efficiency.