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Scaling of small vortices in stably stratified shear flows

Published online by Cambridge University Press:  25 May 2017

Kengo Deguchi Open the ORCID record for Kengo Deguchi [Opens in a new window]
Kengo Deguchi*
Affiliation:
School of Mathematical Sciences, Monash University, VIC 3800, Australia
*
†Email address for correspondence: kengo.deguchi@monash.edu
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Abstract

The present paper treats the large Reynolds number scaling of coherent structures in stably stratified flows sheared between two horizontally placed walls. Three-dimensional steady solutions are used to confirm the theoretical scaling. For small values of the Richardson number, the previously known scaling based on the vortex–wave interaction/self-sustaining process is found to give excellent predictions of the numerical results. When the Richardson number is increased, the maximum size of the vortices is limited by the Ozmidov scale. The largest possible Richardson number to sustain the vortices is predicted to be of order unity when the typical length scale of the vortices reaches the Kolmogorov scale. The minimum-scale vortices are governed by unit Reynolds number Navier–Stokes equations.

JFM classification

Aerodynamics: High-speed flow Instability: Nonlinear instability Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 821 , 25 June 2017 , pp. 582 - 594
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Copyright
© 2017 Cambridge University Press 

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