Lucas, D and Caulfield, CP (2017) Irreversible mixing by unstable periodic orbits in buoyancy dominated stratified turbulence. Journal of Fluid Mechanics, 832. ISSN 0022-1120

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Abstract

We consider turbulence driven by a large-scale horizontal shear in Kolmogorov flow (i.e. with sinusoidal body forcing) and a background linear stable stratification with buoyancy frequency N-B(2) imposed in the third, vertical direction in a fluid with kinematic viscosity nu. This flow is known to be organised into layers by nonlinear unstable steady states, which incline the background shear in the vertical and can be demonstrated to be the finite-amplitude saturation of a sequence of instabilities, originally from the laminar state. Here, we investigate the next order of motions in this system, i.e. the time-dependent mechanisms by which the density field is irreversibly mixed. This investigation is achieved using 'recurrent flow analysis'. We identify (unstable) periodic orbits, which are embedded in the turbulent attractor, and use these orbits as proxies for the chaotic flow. We find that the time average of an appropriate measure of the 'mixing efficiency' of the flow E = chi/(chi + D) (where D is the volume-averaged kinetic energy dissipation rate and chi is the volume-averaged density variance dissipation rate) varies non-monotonically with the time-averaged buoyancy Reynolds numbers (Re-B) over bar = (D) over bar /D(nu N-B(2)), and is bounded above by 1/6, consistently with the classical model of Osborn (J. Phys. Oceanogr., vol. 10 (1), 1980, pp. 83-89). There are qualitatively different physical properties between the unstable orbits that have lower irreversible mixing efficiency at low (Re-B) over bar similar to O(1) and those with nearly optimal E <= 1/6 at intermediate (Re-B) over bar similar to 10. The weaker orbits, inevitably embedded in more strongly stratified flow, are characterised by straining or ' scouring' motions, while the more efficient orbits have clear overturning dynamics in more weakly stratified, and apparently shear-unstable flow.

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at http://dx.doi.org/0.1017/jfm.2017.695 - please refer to any applicable terms of use of the publisher.
Uncontrolled Keywords: fluid mechanics, physics
Subjects: Q Science > QC Physics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 15 Sep 2017 09:19
Last Modified: 23 Nov 2017 11:59
URI: http://eprints.keele.ac.uk/id/eprint/4003

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