Anisotropy and shear-layer edge dynamics of statistically unsteady,stratified turbulence

Abstract

Direct numerical simulation data of an evolving Kelvin-Helmholtz instability have been analyzed in order to characterize the dynamic and kinematic response of shear-generated turbulent flow to imposed stable stratification. Particular emphasis was put on anisotropy and shear-layer edge dynamics in the net kinetic energy decay phase of the Kelvin-Helmholtz evolution. Results indicate a faster increase of small-scale anisotropy compared to large-scale anisotropy. Also, the anisotropy of thermal dissipation differs significantly from that of viscous dissipation. It is found that the Reynolds stress anisotropy increases up to a stratification level roughly corresponding to Ri g ≈ 0.4, but subsequently decreases for higher levels of stratification, most likely due to relaminarization. Coherent large-scale turbulence structures are cylindrical in the center of the shear layer, whereas they become ellipsoidal in the strongly stratified edge-layer region. The structures of the Reynolds stresses are highly one-componental in the center and turn two-componental as stratification increases. Stratification affects all scales, but it seems to affect larger scales to a higher degree than smaller scales and thermal scales more strongly than momentum scales. The effect of strong stable stratification at the edge of the shear layer is highly reminiscent of the non-local pressure effects of solid walls. However, the kinematic blocking inherently associated with impermeable walls is not observed in the edge layer. Vertical momentum flux reversal is found in part of the shear layer. The roles of shear and buoyant production of turbulence kinetic energy are exchanged, and shear production is transferring energy into the mean flow field, which contributes to relaminarization. The change in dynamics near the edge of the shear layer has important implications for predictive turbulence model formulations.

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