On thermohaline convection with linear gradients

Baines, Peter G.; Gill, A. E.

doi:10.1017/s0022112069000553

Cited by 354 publications

(230 citation statements)

References 5 publications

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“…As already discussed by Pojman and Epstein 5,7 and Kalliadasis et al, 49 instability can be observed there even when the density profile is statically stable pointing out to the influence of doublediffusive phenomena ͑also called thermohaline or multicomponent convection͒. [56][57][58][59][60] Concerning the dispersion curves, in quadrant 4, double-diffusive effects are seen to stabilize long wave modes leading to dispersion curves of type I with a finite band of unstable modes, the zero wave number being marginally unstable. 25,49 Such dispersion curves have been measured experimentally for buoyancy-driven deformation of ascending CT fronts.…”

Section: Multicomponent Convectionmentioning

confidence: 82%

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

D’Hernoncourt

Zebib

Wit

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Exothermic autocatalytic fronts traveling in the gravity field can be deformed by buoyancy-driven convection due to solutal and thermal contributions to changes in the density of the product versus the reactant solutions. We classify the possible instability mechanisms, such as Rayleigh-Bénard, Rayleigh-Taylor, and double-diffusive mechanisms known to operate in such conditions in a parameter space spanned by the corresponding solutal and thermal Rayleigh numbers. We also discuss a counterintuitive instability leading to buoyancy-driven deformation of statically stable fronts across which a solute-light and hot solution lies on top of a solute-heavy and colder one. The mechanism of this chemically driven instability lies in the coupling of a localized reaction zone and of differential diffusion of heat and mass. Dispersion curves of the various cases are analyzed. A discussion of the possible candidates of autocatalytic reactions and experimental conditions necessary to observe the various instability scenarios is presented. © 2007 American Institute of Physics. ͓DOI: 10.1063/1.2405129͔It is common knowledge that light fluids rise while heavy fluids sink in the gravity field. Buoyant convection due to a hydrodynamic Rayleigh-Taylor instability can therefore be triggered if a heavy solution lies on top of a lighter one. Rayleigh-Bénard convection appears when a fluid is heated from below. Convection can also result from double-diffusive instabilities of a statically stable density stratification if solutal and thermal effects are in competition. However, it is expected that a stratification of a solute-light and hot fluid over a solute-heavy and cold one should always be stable. Here we show that chemical reactions can change this intuitive picture and trigger convection even in cases where concentration and heat both contribute to a stable density stratification. We find that the balance between intrinsic thermal and solutal density gradients initiated by a spatially localized reaction zone and double-diffusive mechanisms are at the origin of a new convective instability of stable density stratifications the mechanism of which is explained by a displaced particle argument. We also classify the stability properties and dispersion curves to be observed for various classes of exothermic chemical fronts depending whether they ascend or descend in the gravity field and whether their solutal and thermal contributions to the density jump across the front are cooperative or antagonistic.

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Section: Multicomponent Convectionmentioning

confidence: 82%

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

D’Hernoncourt

Zebib

Wit

2007

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…The conditions required for the DD instability to develop have since been generalized (e.g. Veronis 1965;Baines & Gill 1969), showing that only two density-contributing scalars with different molecular diffusivities are required, provided that one exhibits a gravitationally unstable stratification, thus providing the energy source for the instability. Two fundamentally different regimes exist depending on whether T, which we shall take as the faster diffusing scalar (not necessarily temperature), or S, slower where ρ 0 is a constant reference density, and T and S are henceforth given in density units.…”

Section: Introductionmentioning

confidence: 99%

Simulations of a double-diffusive interface in the diffusive convection regime

2012

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Three-dimensional direct numerical simulations are performed that give us an in-depth account of the evolution and structure of the double-diffusive interface. We examine the diffusive convection regime, which, in the oceanographically relevant case, consists of relatively cold fresh water above warm salty water. A 'double-boundary-layer' structure is found in all of the simulations, in which the temperature (T) interface has a greater thickness than the salinity (S) interface. Therefore, thin gravitationally unstable boundary layers are maintained at the edges of the diffusive interface. The TS-interface thickness ratio is found to scale with the diffusivity ratio in a consistent manner once the shear across the boundary layers is accounted for. The turbulence present in the mixed layers is not able to penetrate the stable stratification of the interface core, and the TS-fluxes through the core are given by their molecular diffusion values. Interface growth in time is found to be determined by molecular diffusion of the S-interface, in agreement with a previous theory. The stability of the boundary layers is also considered, where we find boundary layer Rayleigh numbers that are an order of magnitude lower than previously assumed.

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“…Baines & Gill (1969) also found that the system is stable to fingering convection, unless 1 < R 0 < τ −1 . While our particular problem does have a constant background temperature gradient, the compositional gradient clearly varies with z, so their result cannot formally be applied here.…”

Section: The Onset Of Fingering Instabilitymentioning

confidence: 88%

“…Baines & Gill (1969) showed that the stability of a system with constant background temperature and compositional gradients, and in the absence of settling/levitation, is uniquely determined by Pr and τ , as well as the value of the density ratio R 0 , defined as…”

Section: The Onset Of Fingering Instabilitymentioning

confidence: 99%

Fingering Convection Induced by Atomic Diffusion in Stars: 3d Numerical Computations and Applications to Stellar Models

Zemskova

Garaud

Deal

et al. 2014

ApJ

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Iron-rich layers are known to form in the stellar subsurface through a combination of gravitational settling and radiative levitation. Their presence, nature, and detailed structure can affect the excitation process of various stellar pulsation modes and must therefore be modeled carefully in order to better interpret Kepler asteroseismic data. In this paper, we study the interplay between atomic diffusion and fingering convection in A-type stars, as well as its role in the establishment and evolution of iron accumulation layers. To do so, we use a combination of three-dimensional idealized numerical simulations of fingering convection (which neglect radiative transfer and complex opacity effects) and one-dimensional realistic stellar models. Using the three-dimensional simulations, we first validate the mixing prescription for fingering convection recently proposed by Brown et al. (within the scope of the aforementioned approximation) and identify what system parameters (total mass of iron, iron diffusivity, thermal diffusivity, etc.) play a role in the overall evolution of the layer. We then implement the Brown et al. prescription in the Toulouse-Geneva Evolution Code to study the evolution of the iron abundance profile beneath the stellar surface. We find, as first discussed by Théado et al., that when the concurrent settling of helium is ignored, this accumulation rapidly causes an inversion in the mean molecular weight profile, which then drives fingering convection. The latter mixes iron with the surrounding material very efficiently, and the resulting iron layer is very weak. However, taking helium settling into account partially stabilizes the iron profile against fingering convection, and a large iron overabundance can accumulate. The opacity also increases significantly as a result, and in some cases it ultimately triggers dynamical convection. The direct effects of radiative acceleration on the dynamics of fingering convection (especially in the nonlinear regime) remain to be added in the future to improve the quantitative predictions of the model.

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On thermohaline convection with linear gradients

Cited by 354 publications

References 5 publications

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

On the classification of buoyancy-driven chemo-hydrodynamic instabilities of chemical fronts

Simulations of a double-diffusive interface in the diffusive convection regime

Fingering Convection Induced by Atomic Diffusion in Stars: 3d Numerical Computations and Applications to Stellar Models

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