Multiscale equations for strongly stratified turbulent flows

Strongly stratified turbulent shear flows are of fundamental importance owing to their widespread occurrence and their impact on diabatic mixing, yet direct numerical simulations of such flows remain challenging. Here, a reduced, multiscale description of turbulent shear flows in the presence of strong stable density stratification is derived via asymptotic analysis of the governing Boussinesq equations. The analysis explicitly recognizes the occurrence of dynamics on disparate spatiotemoporal scales, and yields simplified partial differential equations governing the coupled evolution of slowly-evolving small aspect-ratio (`pancake') modes and isotropic, strongly non-hydrostatic stratified-shear (e.g. Kelvin--Helmholtz) instability modes. The reduced model is formally valid in the physically-relevant regime in which the aspect-ratio of the pancake structures tends to zero in direct proportion to the horizontal Froude number. Relative to the full Boussinesq equations, the model offers both computational and conceptual advantages.