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

Abstract

We study the morphology of Eulerian vortical structures and their interaction with density interfaces in increasingly turbulent stably stratified shear layers. We analyse the three-dimensional, simultaneous velocity and density fields obtained in the stratified inclined duct laboratory experiment (SID). We track, across 15 datasets, the evolution of coherent structures from pre-turbulent Holmboe waves, through intermittent turbulence, to full turbulence and mixing. We use the rortex–shear decomposition of the local vorticity vectors into a rortex vector capturing rigid-body rotation and a shear vector. We describe the morphology of ubiquitous hairpin-like vortical structures (revealed by the rortex), similar to those commonly observed in boundary-layer turbulence. These are born as relatively weak vortices around the strong three-dimensional shearing structures of confined Holmboe waves, and gradually strengthen and deform under increasing turbulence, transforming into pairs of upward- and downward-pointing hairpins propagating in opposite directions on the top and bottom edge of the shear layer. The pair of legs for each hairpin are counter-rotating and entrain fluid laterally and vertically, whereas their arched-up ‘heads’, which are transverse vortices, entrain fluid vertically. We then elucidate how this large-scale vortex morphology stirs and mixes the density field. Essentially, vortices located at the sharp density interface on either edge of the mixing layer (mostly hairpin heads) engulf blobs of unmixed fluid into the mixing layer, whereas vortices inside the mixing layer (mostly hairpin legs) further stir it, generating strong, small-scale shear, enhancing mixing. These findings provide new insights into the role of turbulent coherent structures in shear-driven stratified mixing.

Stratified inclined duct: direct numerical simulations

“…The flow regimes are (ordered by increasing θ Re): laminar two-layer flow, interfacial waves, intermittent turbulence with increased interfacial mixing and eventually full turbulence with significant mixing. Much insight has already been gained through experimental studies of these regimes and of their transitions (Meyer & Linden 2014;Lefauve & Linden 2020a, 2022a, of their energetics and mixing properties (Lefauve, Partridge & Linden 2019;Lefauve & Linden 2022b) and of their respective coherent structures (Lefauve et al 2018;Jiang et al 2022).…”

How does turbulence mix a stratified fluid?

“…RL, longitudinal rortex (green) with R primarily along ; RT, transverse rortex (magenta) with R primarily along (from Jiang et al. 2022). …”

“…But these experiments are usually limited in Reynolds number and in the details of the flow to be explored, and are restricted to point-wise measurements, or more recently to planar measurements, and only snapshots are available rather than time-resolved measurements. The research presented by Jiang et al (2022) reports on the use of a very advanced experimental facility to study stratified shear flows, the stratified inclined duct (SID). In addition to the systematic variation of two key non-dimensional flow parameters, allowing a broad range of dynamics for study, the facility allows for the measurement of the three-component velocity and the density fields in three dimensions, and with high spatial and temporal resolutions, essentially coming close to the capabilities of direct numerical simulation, but at Prandtl numbers characteristic of geophysical flows.…”

Geometry of stratified turbulent mixing: local alignment of the density gradient with rotation, shear and viscous dissipation

“…Using simultaneous 3-D velocity and density data in the ‘stratified inclined duct’ (SID) laboratory experiment, Jiang et al (2022) analysed the morphology of coherent (Eulerian) vortical structures and their evolution from preturbulent Holmboe waves to fully developed sheared turbulence. They explained how turbulent hairpin vortices across the density interface engulf unmixed fluid into the stratified interface, while vortices within the shear layer generate further stirring and small-scale shear, enhancing irreversible mixing.…”

“…The objective of this paper is to tackle these issues by using the same datasets as Jiang et al. (2022) and quantifying the relation between kinematic rotational and shearing flow structures and the dynamics and energetics of the flow, an open question (Riley 2022) essential to improve parametrisations. Specifically, we will address the two following questions.…”