Impact of alignments between fluctuating and mean density gradients on the scale-dependent energetics of stably stratified turbulence

Abstract

Non-trivial alignments between vorticity and the strain-rate tensor play an important role in the evolution of velocity gradients and the energy cascade in isotropic turbulence. Here we explore how alignments between the fluctuating and mean density gradients impact the mechanisms governing the turbulent kinetic energy (TKE) and available potential energy (APE) across scales in stably stratified turbulence. This is motivated by analytical results that demonstrate a connection between them, and is conducted using direct numerical simulations (DNS) of statistically stationary, stably stratified turbulence for $Pr = 1, 7, 50$ in the strongly stratified regime. After demonstrating how the gradient field alignments depend on scale and $Pr$, we show that the alignments are intimately connected to the reversal of the buoyancy flux at small-scales, and that regions of strong alignment and misalignment correspond to regions where the horizontal TKE inter-scale flux becomes weak. The same is also true of the APE flux, except that at larger scales, regions of strong alignment are associated with an upscale APE flux. The TKE and APE dissipation rates, and the mixing coefficient also show a strong dependence on the alignment, especially for $Pr=1$. Finally, we explore the connection between the local alignment and stability of the flow, and we find a non-trivial relationship, with regions of strong alignment surprisingly occurring most often in stable regions. This demonstrates that the dynamical significance of the alignments on the flow energetics cannot be understood through a simple connection between the local alignments and local stability of the flow.