Equilibration of weakly nonlinear salt fingers
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Authors
Radko, Timour
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Date of Issue
2010
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Abstract
An analytical model is developed to explain the equilibration mechanism of the salt
finger instability in unbounded temperature and salinity gradients. The theory is based
on the weakly nonlinear asymptotic expansion about the point of marginal instability.
The proposed solutions attribute equilibration of salt fingers to a combination of
two processes: (i) the triad interaction and (ii) spontaneous development of the
mean vertical shear. The non-resonant triad interactions control the equilibration of
linear growth for moderate and large values of Prandtl number (Pr) and for slightly
unstable parameters. For small Pr and/or rigorous instabilities, the mean shear effects
become essential. It is shown that, individually, neither the mean field nor the triad
interaction models can accurately describe the equilibrium patterns of salt fingers
in all regions of the parameter space. Therefore, we propose a new hybrid model,
which represents both stabilizing effects in a single framework. The resulting solutions
agree with the fully nonlinear numerical simulations over a wide range of governing
parameters.
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Article
Description
The article of record as published may be found at http://dx.doi.org/10.1017/S0022112009992552
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Department
Oceanography
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Citation
J. Fluid Mech. (2010), vol. 645, pp. 121–143.
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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.