Dynamics of fingering convection I: Small-scale fluxes and large-scale instabilities
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Authors
Traxler, A.
Stellmach, S.
Garaud, P.
Radko, T.
Brummell, N.
Subjects
double-diffusive convection
geophysical and geological flows
geophysical and geological flows
Advisors
Date of Issue
2011
Date
2011
Publisher
Language
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 two 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 gamma-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 gamma-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.
Type
Description
The article of record as published may be found at http://dx.doi.org/10.1017/jfm.2011.98
Series/Report No
Department
Oceanography