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A multi-parameter criterion for layer formation in a stratified shear flow using sorted buoyancy coordinates

Published online by Cambridge University Press:  23 June 2017

J. R. Taylor Open the ORCID record for J. R. Taylor [Opens in a new window]  and
Q. Zhou Open the ORCID record for Q. Zhou [Opens in a new window]
J. R. Taylor*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
Q. Zhou
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Centre for Mathematical Sciences, Wilberforce Road, Cambridge CB3 0WA, UK
*
†Email address for correspondence: J.R.Taylor@damtp.cam.ac.uk
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Abstract

Here, we examine the conditions for layer formation in a stratified shear flow. We reformulate the conditions for amplification of small perturbations to a uniform stratification first proposed by Phillips (Deep Sea Research and Oceanographic Abstracts, vol. 19, 1972, pp. 79–81, Elsevier) and Posmentier (J. Phys. Oceanogr., vol. 7 (2), 1977, pp. 298–300) using the sorted buoyancy coordinates introduced by Nakamura (J. Atmos. Sci., vol. 53 (11), 1996, pp. 1524–1537) and Winters & D’Asaro (J. Fluid Mech., vol. 317, 1996, pp. 179–193). We consider the possible dependence of the effective diffusivity on three non-dimensional parameters, the gradient Richardson number, the buoyancy Reynolds number and the Prandtl number, and obtain a simple expression for conditions favourable for layer formation. The new framework is applied to direct numerical simulations of stratified shear flow. We then apply a recent multi-parameter parameterization developed by Salehipour et al. (Geophys. Res. Lett., vol. 43 (7), 2016, pp. 3370–3379), which suggests that layer formation is favoured for large Prandtl numbers and moderate to large values of the gradient Richardson and buoyancy Reynolds numbers.

JFM classification

Turbulent Flows: Stratified turbulence Turbulent Flows: Turbulent Flows
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 823 , 25 July 2017 , R5
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Copyright
© 2017 Cambridge University Press 

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