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Dynamics of fingering convection. Part 1 Small-scale fluxes and large-scale instabilities

Published online by Cambridge University Press:  19 April 2011

A. TRAXLER ,
S. STELLMACH ,
P. GARAUD ,
T. RADKO  and
N. BRUMMELL
A. TRAXLER*
Affiliation:
Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA 96064, USA
S. STELLMACH
Affiliation:
Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA 96064, USA Institut für Geophysik, Westfälische Wilhelms-Universität Münster, D-48149 Münster, Germany Institute of Geophysics and Planetary Physics, University of California, Santa Cruz, CA 96064, USA
P. GARAUD
Affiliation:
Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA 96064, USA
T. RADKO
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA
N. BRUMMELL
Affiliation:
Applied Mathematics and Statistics, Baskin School of Engineering, University of California, Santa Cruz, CA 96064, USA
*
†Email address for correspondence: atraxler@soe.ucsc.edu
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Abstract

Double-diffusive instabilities are often invoked to explain enhanced transport in stably stratified fluids. The most-studied natural manifestation of this process, fingering convection, commonly occurs in the ocean's thermocline and typically increases diapycnal mixing by 2 orders of magnitude over molecular diffusion. Fingering convection is also often associated with structures on much larger scales, such as thermohaline intrusions, gravity waves and thermohaline staircases. In this paper, we present an exhaustive study of the phenomenon from small to large scales. We perform the first three-dimensional simulations of the process at realistic values of the heat and salt diffusivities and provide accurate estimates of the induced turbulent transport. Our results are consistent with oceanic field measurements of diapycnal mixing in fingering regions. We then develop a generalized mean-field theory to study the stability of fingering systems to large-scale perturbations using our calculated turbulent fluxes to parameterize small-scale transport. The theory recovers the intrusive instability, the collective instability and the γ-instability as limiting cases. We find that the fastest growing large-scale mode depends sensitively on the ratio of the background gradients of temperature and salinity (the density ratio). While only intrusive modes exist at high density ratios, the collective and γ instabilities dominate the system at the low density ratios where staircases are typically observed. We conclude by discussing our findings in the context of staircase-formation theory.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 677 , 25 June 2011 , pp. 530 - 553
Copyright
Copyright © Cambridge University Press 2011

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