Salt-finger convection provides a key mixing process in geophysical and astrophysical fluid flows. Because of its small characteristic spatial scale and slow diffusive time scale, this process must be parameterized in geophysical and astrophysical models, where relations linking background gradients to fluxes are required. To obtain such relations, most authors study the dependence of temperature and salinity fluxes on fixed background gradients. Using the reduced model derived by Xie et al. [“A reduced model for salt-finger convection in the small diffusivity ratio limit,” Fluids 2(1), 6 (2017)] for salt-finger convection in the limit of small diffusivity and large density ratios, this paper considers the conjugate problem where the fluxes are fixed, but the mean gradients are permitted to adjust in response. In small domains, the fixed-flux condition leads to stable single-mode solutions, which are not achievable with fixed-gradient conditions. In large domains, with statistically steady saturated states, the relations between mean fluxes and mean gradients are identical for both sets of conditions. The fixed-flux condition provides a new perspective for understanding the resulting statistically steady states by identifying two distinct regimes with the same dissipation rate. We find that the statistically steady dynamics select the state with the smaller Rayleigh ratio Ra subject to the constraint Ra > 1, ensuring that the background state is linearly unstable. The fixed-flux formulation results in a more potent restoring mechanism toward the statistically steady state, with a smaller variance, skewness, and characteristic time scale than in the fixed-gradient setup. This distinctive feature can be used as a diagnostic to determine whether in situ salt-finger convection is flux-driven or gradient-driven.
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December 2020
Research Article|
December 07 2020
Fixed-flux salt-finger convection in the small diffusivity ratio limit
Special Collection:
Interfaces and Mixing, and Beyond
Jin-Han Xie
;
Jin-Han Xie
a)
1
Department of Mechanics and Engineering Science at College of Engineering, LTCS and BIC-ESAT, Peking University
, Beijing 100871, People’s Republic of China
a)Author to whom correspondence should be addressed: [email protected]
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Keith Julien;
Keith Julien
b)
2
Department of Applied Mathematics, University of Colorado
, Boulder, Colorado 80309, USA
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Edgar Knobloch
Edgar Knobloch
c)
3
Department of Physics, University of California
, Berkeley, California 94720, USA
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a)Author to whom correspondence should be addressed: [email protected]
b)
Electronic mail: [email protected]
c)
Electronic mail: [email protected]
Note: This paper is part of the Special Topic, Interfaces and Mixing, and Beyond.
Physics of Fluids 32, 126601 (2020)
Article history
Received:
September 27 2020
Accepted:
November 17 2020
Citation
Jin-Han Xie, Keith Julien, Edgar Knobloch; Fixed-flux salt-finger convection in the small diffusivity ratio limit. Physics of Fluids 1 December 2020; 32 (12): 126601. https://doi.org/10.1063/5.0031071
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