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A localized turbulent mixing layer in a uniformly stratified environment

Published online by Cambridge University Press:  18 June 2018

Tomoaki Watanabe Open the ORCID record for Tomoaki Watanabe [Opens in a new window] ,
James J. Riley ,
Koji Nagata Open the ORCID record for Koji Nagata [Opens in a new window] ,
Ryo Onishi  and
Keigo Matsuda
Tomoaki Watanabe*
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
James J. Riley
Affiliation:
Department of Mechanical Engineering, University of Washington, Seattle 98195, USA
Koji Nagata
Affiliation:
Department of Aerospace Engineering, Nagoya University, Nagoya 464-8603, Japan
Ryo Onishi
Affiliation:
Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
Keigo Matsuda
Affiliation:
Earth Simulator Center, Japan Agency for Marine-Earth Science and Technology, Yokohama 236-0001, Japan
*
†Email address for correspondence: [email protected]
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Abstract

Localized turbulence bounded by non-turbulent flow in a uniformly stratified environment is studied with direct numerical simulations of stably stratified shear layers. Of particular interest is the turbulent/non-turbulent interfacial (TNTI) layer, which is detected by identifying the turbulent region in terms of its potential vorticity. Fluid near the outer edge of the turbulent region gains potential vorticity and becomes turbulent by diffusion arising from both viscous and molecular effects. The flow properties near the TNTI layer change depending on the buoyancy Reynolds number near the interface, $Re_{bI}$. The TNTI layer thickness is approximately 13 times the Kolmogorov length scale for large $Re_{bI}$ ($Re_{bI}\gtrsim 30$), consistent with non-stratified flows, whereas it is almost equal to the vertical length scale of the stratified flow, $l_{vI}=l_{hI}Re^{-1/2}$ (here $l_{hI}$ is the horizontal length scale near the TNTI layer, and $Re$ is the Reynolds number), in the low-$Re_{bI}$ regime ($Re_{bI}\lesssim 2$). Turbulent fluid is vertically transported towards the TNTI layer when $Re_{bI}$ is large, sustaining the thin TNTI layer with large buoyancy frequency and mean shear. This sharpening effect is weakened as $Re_{bI}$ decreases and eventually becomes negligible for very low $Re_{bI}$. Overturning motions occur near the TNTI layer for large $Re_{bI}$. The dependence on buoyancy Reynolds number is related to the value of $Re_{bI}$ near the TNTI layer, which is smaller than the value deep inside the turbulent core region. An imprint of the internal gravity waves propagating in the non-turbulent region is found for vorticity within the TNTI layer, inferring an interaction between turbulence and internal gravity waves. The wave energy flux causes a net loss of the kinetic energy in the turbulent core region bounded to the TNTI layer, and the amount of kinetic energy extracted from the turbulent region by internal gravity waves is comparable to the amount dissipated in the turbulent region.

JFM classification

Geophysical and Geological Flows: Internal waves Turbulent Flows: Shear layer turbulence Turbulent Flows: Stratified turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 849 , 25 August 2018 , pp. 245 - 276
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Copyright
© 2018 Cambridge University Press 

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