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Non-invasive turbulent mixing across a density interface in a turbulent Taylor–Couette flow

Published online by Cambridge University Press:  04 November 2010

ANDREW W. WOODS ,
C. P. CAULFIELD ,
J. R. LANDEL  and
A. KUESTERS
ANDREW W. WOODS*
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
C. P. CAULFIELD
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
J. R. LANDEL
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
A. KUESTERS
Affiliation:
BP Institute, University of Cambridge, Madingley Road, Cambridge CB3 0EZ, UK
*
†Email address for correspondence: [email protected]
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Abstract

In this paper, we present new experimental measurements of the turbulent transport of salt across an interface between two layers of fluid of equal depth but different salinities. The fluid is confined to a cylindrical annulus with a vertical axis. The outer cylinder is stationary and the inner cylinder rotates to produce a turbulent flow field consisting of an approximately irrotational mean azimuthal flow, with narrow boundary layers on the inner and outer cylinders. We focus on the limit of high-Richardson-number flow, defined as Ri = gΔρH/(ρ0u2rms), where ρ0 is a reference density, Δρ is the time-dependent difference of the layers' mean densities, urms is the root mean square of the turbulent velocity fluctuations and H is the layer depth. The mean flow has Reynolds number of the order of 104−105, and the turbulent fluctuations in the azimuthal and radial directions have root-mean-square speed of order 10% of the mean azimuthal flow. Measurements based on our experimental system show that when the Richardson number is in the range 7 < Ri < 200, the interface between the two layers remains sharp, each layer remains well mixed, and the vertical flux of salt between the layers, Fs ~(1.15 ± 0.15)Ri−1𝒜(H/ΔR)urmsΔS, where ΔS is the spatially-averaged time-dependent salinity difference between the layers and in general 𝒜(H/ΔR) is a dimensionless function of the tank aspect ratio, here taken to be unity, with ΔR being the gap width of the annulus. The salt transport appears to be caused by turbulent eddies scouring and sharpening the interface and implies a constant rate of conversion of the turbulent kinetic energy to potential energy, independent of the density contrast between the layers. For smaller values of Ri, the flow regime changes qualitatively, with eddies penetrating the interface, causing fluid in the two layers to co-mingle and rapidly homogenize.

JFM classification

Geophysical and Geological Flows: Stratified flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 663 , 25 November 2010 , pp. 347 - 357
Copyright
Copyright © Cambridge University Press 2010

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