Experimental properties of continuously forced, shear-driven, stratified turbulence. Part 1. Mean flows, self-organisation, turbulent fractions

Abstract

We study the experimental properties of exchange flows in a stratified inclined duct, which are simultaneously turbulent, strongly stratified by a mean vertical density gradient, driven by a mean vertical shear, and continuously forced by gravity. We focus on the ‘core’ shear layer away from the duct walls, where these flows are excellent experimentally realisable approximations of canonical hyperbolic-tangent stratified shear layers, whose forcing allows mean and turbulent properties to reach quasi-steady states. We analyse state-of-the-art data sets of the time-resolved density and velocity in three-dimensional subvolumes of the duct in 16 experiments covering a range of flow regimes (Holmboe waves, intermittent turbulence, full turbulence). In this Part 1 we first reveal the permissible regions in the multidimensional parameter space (Reynolds number, bulk Richardson number, velocity-to-density layer thickness ratio), and their link to experimentally controllable parameters. Reynolds-averaged balances then reveal the subtle momentum forcing and dissipation mechanisms in each layer, the broadening or sharpening of the density interface, and the importance of the streamwise non-periodicity of these flows. Mean flows suggest a tendency towards self-similarity of the velocity and density profiles with increasing turbulence, and gradient Richardson number statistics support prior ‘internal mixing’ theories of ‘equilibrium Richardson number’, ‘marginal stability’ and ‘self-organised criticality’. Turbulent volume fractions based on enstrophy and overturn thresholds quantify the nature of turbulence between different regimes in different regions of parameter space, while highlighting the challenges of obtaining representative statistics in spatiotemporally intermittent flows. These insights may stimulate and assist the development of numerical simulations with a higher degree of experimental realism.