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Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

Published online by Cambridge University Press:  21 February 2017

Philippe Odier  and
Robert E. Ecke
Philippe Odier*
Affiliation:
Université de Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, F-69342 Lyon, France
Robert E. Ecke
Affiliation:
Center for Nonlinear Studies and Condensed Matter & Magnetic Sciences, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
*
†Email address for correspondence: [email protected]
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Abstract

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. We explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of $Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $Ri$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $Ri$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $Ri$ but decreases rapidly as $Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. The distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.

JFM classification

Boundary Layers: Free shear layers Geophysical and Geological Flows: Geophysical and Geological Flows Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 815 , 25 March 2017 , pp. 243 - 256
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Copyright
© 2017 Cambridge University Press 

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