Applicability and failure of the flux-gradient laws in double-diffusive convection
Abstract
Double-diffusive flux-gradient laws are commonly used to describe the development
of large-scale structures driven by salt fingers – thermohaline staircases, collective
instability waves and intrusions. The flux-gradient model assumes that the vertical
transport is uniquely determined by the local background temperature and salinity
gradients. While flux-gradient laws adequately capture mixing characteristics on scales
that greatly exceed those of primary double-diffusive instabilities, their accuracy
rapidly deteriorates when the scale separation between primary and secondary
instabilities is reduced. This study examines conditions for the breakdown of the
flux-gradient laws using a combination of analytical arguments and direct numerical
simulations. The applicability (failure) of the flux-gradient laws at large (small)
scales is illustrated through the example of layering instability, which results in
the spontaneous formation of thermohaline staircases from uniform temperature and
salinity gradients. Our inquiry is focused on the properties of the ‘point-of-failure’
scale (Hpof ) at which the vertical transport becomes significantly affected by the
non-uniformity of the background stratification. It is hypothesized that Hpof can
control some key characteristics of secondary double-diffusive phenomena, such
as the thickness of high-gradient interfaces in thermohaline staircases. A more
general parametrization of the vertical transport – the flux-gradient-aberrancy law –
is proposed, which includes the selective damping of relatively short wavelengths
that are inadequately represented by the flux-gradient models. The new formulation is
free from the unphysical behaviour of the flux-gradient laws at small scales (e.g. the
ultraviolet catastrophe) and can be readily implemented in theoretical and large-scale
numerical models of double-diffusive convection.
Description
The article of record as published may be found at http://dx.doi.org/10.1017/jfm.2014.244
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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