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.

Critical balance and scaling of strongly stratified turbulence at low Prandtl number

“…Examining the role of vertical shear instabilities in the turbulence offers an alternative physical interpretation of the scaling results. Many experimental and numerical studies in the geophysical regime find evidence suggesting that turbulent structures are organized to be marginally unstable to local vertical shear instabilities, a behaviour thought to be closely related to self-organized criticality (Smyth & Moum 2013;Salehipour et al 2018;Smyth et al 2019;Chini et al 2022;Lefauve & Linden 2022). A heuristic argument for such behaviour is that the vertical shear of a turbulent eddy will generally be driven towards the marginal value of the shear for instability.…”

“…Many important features of the unity Prandtl-number regime are becoming better understood from a combination of numerical experiments (Waite & Bartello 2004;Brethouwer et al 2007;Riley & Lindborg 2010;Maffioli & Davidson 2016;Lucas, Caulfield & Kerswell 2017;de Bruyn Kops & Riley 2019), observational data Riley & Lindborg 2008;Falder, White & Caulfield 2016;Lefauve & Linden 2022) and theoretical developments (Billant & Chomaz 2001;Lindborg 2006;Chini et al 2022). Strongly stratified turbulence with Pr = O(1) forced at some horizontal length scale leads to emergent vertical scales set by the stratification and exhibits two distinct inertial ranges that transfer energy from the large forcing scales to the small viscous and thermal scales where it is dissipated.…”

“…Below the Ozmidov scale, the turbulence is isotropic down to the diffusive scales. The properties of the energy cascade, relevant dimensionless parameters and scaling relations for the emergent vertical scales are now fairly well understood, although many further questions remain, such as on the efficiency of mixing (Gregg et al 2018;Monismith, Koseff & White 2018;Legg 2021) and the origin of self-organized criticality (Smyth & Moum 2013;Salehipour, Peltier & Caulfield 2018;Smyth, Nash & Moum 2019;Chini et al 2022;Lefauve & Linden 2022).…”

The evolution of coherent vortical structures in increasingly turbulent stratified shear layers

“…(2018 a , 2019) and Partridge et al. (2019), in this paper we use the slightly modified datasets of Lefauve & Linden (2022 a , b ) (hereafter LL22a,b). These modifications are explained in LL22a (see their §§ 3.3–3.5 and figure 1) and are summarised as follows.…”

“…Finally, the relative strength of rorticity versus shear also increases (see the colour bars and isosurface values in the caption), indicating an increasing correlation between rortices and turbulent mixing. Although we do not quantify mixing explicitly in this paper, we refer the reader to Lefauve & Linden (2022 a ) and Lefauve & Linden (2022 b ) who did so in these 15 datasets using a variety of measures.…”