Fingering Convection: the Interplay of Small and Large Scales

Paparella, Francesco

doi:10.1111/j.1749-6632.2000.tb06170.x

Cited by 2 publications

(1 citation statement)

References 27 publications

(38 reference statements)

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“…The laboratory values of C S have been found to overestimate the oceanic fluxes by at least an order of magnitude, a discrepancy that may indicate that the effective exponent of the flux law realized in the oceanic conditions exceeds 4/3. Direct numerical simulations by Ozgokmen, Essenkov & Olson (1998) resulted in an approximate agreement with the 4/3 law over most of the explored parameter range, but with large deviations at high and low values of S, whereas simulations in Paparella (2000) suggest that the exponent of the flux law consistently exceeds 4/3 and could be as high as b = 2. The reader is referred to Kunze (2003) for a discussion of these and other simple models of interfacial fluxes.…”

Section: Flux Lawsmentioning

confidence: 98%

What determines the thickness of layers in a thermohaline staircase?

Radko¹

2005

J. Fluid Mech.

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A simple theory is developed for the equilibrium height of steps in a thermohaline staircase. The model is based on a linear stability analysis for a series of salt-finger interfaces, which reveals a tendency for the staircase to evolve in time until the characteristic thickness of layers reaches a critical value (H 0 ). Relatively thin layers successively merge as a result of the parametric variation of the heat/salt flux ratio (γ ), but these mergers cease when the thickness of layers exceeds H 0 . The equilibration of thick steps in our model is caused by the slight inhomogeneity of the convecting layers which has a stabilizing effect on the staircase. The instability theory is successfully tested against fully nonlinear numerical simulations and is qualitatively consistent with oceanic observations.

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Section: Flux Lawsmentioning

confidence: 98%

What determines the thickness of layers in a thermohaline staircase?

Radko¹

2005

J. Fluid Mech.

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The effect of concentration-dependent diffusion on double-diffusive instability

et al. 2022

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The article studies the stability of a two-layer miscible system to the double-diffusive instability. The system is placed in a vertical Hele–Shaw cell and is composed of two homogeneous aqueous solutions initially separated by a narrow transient zone. We have restricted our consideration to the initially stable density stratification that precludes the Rayleigh–Taylor instability. The main objective of the study is to elucidate the effect of a concentration-dependent diffusion coefficient, which has been commonly ignored by researchers. Assuming linear dependence of the diffusion coefficient of each solute and using Picard's iteration scheme, we have derived a closed-form analytical expression for the time-dependent density profile. This permits the stability boundary to be established for a two-layer system with respect to the double-diffusive instability by taking into account the effect of a concentration-dependent diffusion coefficient. The obtained analytical result has been substantiated by the results of direct numerical simulation. The experiments have shown that a successive increase in the concentrations of both solutes, with their ratio remaining unchanged, can lead to opposite results. In the case of a NaNO3-H2SO4 pair, the two-layer system, being stable at low concentrations, becomes unstable as the concentrations proportionally increase, giving rise to convective motion in the form of salt fingers. On the contrary, a two-layer system consisting of LiCl and NaNO3 solutions is stabilized with increasing concentrations of dissolved substances. A further increase in the concentrations of these substances causes mechanical equilibrium breaking and subsequent formation of the so-called diffusive-layer convection. The experimental results are in good agreement with the theoretical predictions.

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Fingering Convection: the Interplay of Small and Large Scales

Cited by 2 publications

References 27 publications

What determines the thickness of layers in a thermohaline staircase?

What determines the thickness of layers in a thermohaline staircase?

The effect of concentration-dependent diffusion on double-diffusive instability

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