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Theory for differential transport of scalars in sheared stratified turbulence

Published online by Cambridge University Press:  12 February 2009

P. RYAN JACKSON  and
CHRIS R. REHMANN
P. RYAN JACKSON*
Affiliation:
Applied Ocean Physics and Engineering Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USApjackson@whoi.edu
CHRIS R. REHMANN
Affiliation:
374 Town Engineering Building, Department of Civil, Construction, and Environmental Engineering, Iowa State University, Ames, IA 50014, USArehmann@iastate.edu
*
†Present address and email address for correspondence: US Geological Survey, Illinois Water Science Center, 1201 W. University Ave, Urbana, IL 61801, USA. pjackson@usgs.gov
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Abstract

Scalars with different molecular diffusivities can be transported at different rates in a strongly stratified, weakly turbulent flow. Rapid distortion theory (RDT) is used to examine the mechanisms responsible for differential diffusion of scalars in a sheared stratified flow. The theory, which applies when the flow is strongly stratified, predicts upgradient flux and its wavenumber dependence, which previous direct numerical simulations have shown to be important in differential diffusion. The net effect of shear on differential diffusion depends on the Grashof number, or the relative importance of buoyancy and viscous effects. RDT also allows the effects of the density ratio, Schmidt number, Lewis number, scalar activity and mean shear to be examined without the high computational cost of direct numerical simulation. RDT predicts that differential diffusion will increase with increasing density ratio, but only at low Grashof number. When the Lewis number is fixed, the Grashof number below which differential diffusion occurs decreases with increasing Schmidt number, and when one of the Schmidt numbers is fixed, differential diffusion decreases with increasing Lewis number. Also, differential transport of passive scalars increases when the Schmidt number of the scalar stratifying the flow increases.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 621 , 25 February 2009 , pp. 1 - 21
Copyright
Copyright © Cambridge University Press 2009

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