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Thermohaline layering on the microscale

Published online by Cambridge University Press:  14 January 2019

Timour Radko Open the ORCID record for Timour Radko [Opens in a new window]
Timour Radko*
Affiliation:
Department of Oceanography, Naval Postgraduate School, Monterey, CA 93943, USA
*
†Email address for correspondence: tradko@nps.edu
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Abstract

A theoretical model is developed which illustrates the dynamics of layering instability, frequently realized in ocean regions with active fingering convection. Thermohaline layering is driven by the interplay between large-scale stratification and primary double-diffusive instabilities operating at the microscale – temporal and spatial scales set by molecular dissipation. This interaction is described by a combination of direct numerical simulations and an asymptotic multiscale model. The multiscale theory is used to formulate explicit and dynamically consistent flux laws, which can be readily implemented in large-scale analytical and numerical models. Most previous theoretical investigations of thermohaline layering were based on the flux-gradient model, which assumes that the vertical transport of density components is uniquely determined by their local background gradients. The key deficiency of this approach is that layering instabilities predicted by the flux-gradient model have unbounded growth rates at high wavenumbers. The resulting ultraviolet catastrophe precludes the analysis of such basic properties of layering instability as its preferred wavelength or the maximal growth rate. The multiscale model, on the other hand, incorporates hyperdiffusion terms that stabilize short layering modes. Overall, the presented theory carries the triple advantage of (i) offering an explicit description of the interaction between microstructure and layering modes, (ii) taking into account the influence of non-uniform stratification on microstructure-driven mixing, and (iii) avoiding unphysical behaviour of the flux-gradient laws at small scales. While the multiscale approach to the parametrization of time-dependent small-scale processes is illustrated here on the example of fingering convection, we expect the proposed technique to be readily adaptable to a wide range of applications.

JFM classification

Convection: Double diffusive convection
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 862 , 10 March 2019 , pp. 672 - 695
Copyright
© 2019 Cambridge University Press 

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