Experimental properties of continuously forced, shear-driven, stratified turbulence. Part 2. Energetics, anisotropy, parameterisation

Abstract

In this Part 2 we study further experimental properties of two-layer exchange flows in a stratified inclined duct, which are turbulent, strongly stratified, shear-driven and continuously forced. We analyse the same state-of-the-art data sets using the same ‘core’ shear-layer methodology as in Part 1 (Lefauve & Linden, J. Fluid Mech., vol. 937, 2022, A34), but we focus here on turbulent energetics and mixing statistics. The detailed analysis of kinetic and scalar energy budgets reveals the specificity and scalings of ‘SID turbulence’, while energy spectra provide insight into the current strengths and limitations of our experimental data. The anisotropy of the flow at different scales characterises the turbulent kinetic energy production and dissipation mechanisms of Holmboe waves and overturning turbulence. We then assess standard mixing parameterisation models relying on uniform eddy diffusivities, mixing lengths, flux parameters, buoyancy Reynolds numbers or turbulent Froude numbers, and we compare our representative values with the stratified mixing literature. The dependence of these measures of mixing on controllable flow parameters is also elucidated, providing asymptotic estimates that may be extrapolated to more strongly turbulent flows, quantified by the product of the tilt angle of the duct and the Reynolds number. These insights may serve as benchmark for the future generation of experimental data with superior spatio-temporal resolution required to probe increasingly vigorous turbulence.