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Testing linear marginal stability in stratified shear layers

Published online by Cambridge University Press:  02 February 2018

C. J. Howland Open the ORCID record for C. J. Howland [Opens in a new window] ,
J. R. Taylor Open the ORCID record for J. R. Taylor [Opens in a new window]  and
C. P. Caulfield Open the ORCID record for C. P. Caulfield [Opens in a new window]
C. J. Howland
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
J. R. Taylor
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
C. P. Caulfield*
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: c.p.caulfield@bpi.cam.ac.uk
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Abstract

We use two-dimensional direct numerical simulations of Boussinesq stratified shear layers to investigate the influence of the minimum gradient Richardson number $Ri_{m}$ on the early time evolution of Kelvin–Helmholtz instability to its saturated ‘billow’ state. Even when the diffusion of the background velocity and density distributions is counterbalanced by artificial body forces to maintain the initial profiles, in the limit as $Ri_{m}\rightarrow 1/4$, the perturbation growth rate tends to zero and the saturated perturbation energy becomes small. These results imply, at least for such canonical inflectional stratified shear flows, that ‘marginally unstable’ flows with $Ri_{m}$ only slightly less than 1/4 are highly unlikely to become ‘turbulent’, in the specific sense of being associated with significantly enhanced dissipation, irreversible mixing and non-trivial modification of the background distributions without additional externally imposed forcing.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Instability: Instability Geophysical and Geological Flows: Stratified flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , R4
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Copyright
© 2018 Cambridge University Press 

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