Thermo-Chemical Convection in Planetary Mantles

Thermo-chemical convection is the primary process that controls the large-scale dynamics of the mantle of the Earth and terrestrial planets. Its numerical simulation is one the principal tools for exploiting the constraints posed by geological and geochemical surface observations performed by planetary spacecrafts. In the present work, the authors discuss the modeling of active compositional fields in the framework of solid-state mantle convection using the cylindrical/spherical code Gaia. They compare an Eulerian method based on double-diffusive convection against a Lagrangian, particle-based method. Through a series of increasingly complex benchmark tests, the authors show the superiority of the particle method when it comes to model the advection of compositional interfaces with sharp density and viscosity contrasts. They finally apply this technique to simulate the Rayleigh-Taylor overturn of the Mars’ and Mercury’s primordial magma oceans.

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Applicability and failure of the flux-gradient laws in double-diffusive convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2014.244 ◽

2014 ◽

Vol 750 ◽

pp. 33-72 ◽

Cited By ~ 8

Author(s):

Timour Radko

Keyword(s):

Large Scale ◽

Numerical Models ◽

Vertical Transport ◽

Double Diffusive Convection ◽

Flux Gradient ◽

Salinity Gradients ◽

Diffusive Convection ◽

Small Scales ◽

New Formulation ◽

Double Diffusive

AbstractDouble-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 ($\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}H_{pof}$) at which the vertical transport becomes significantly affected by the non-uniformity of the background stratification. It is hypothesized that$H_{pof} $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.

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Large-scale Langmuir circulation and double-diffusive convection: evolution equations and flow transitions

Journal of Fluid Mechanics ◽

10.1017/s0022112094002521 ◽

1994 ◽

Vol 276 ◽

pp. 189-210 ◽

Cited By ~ 11

Author(s):

Stephen M. Cox ◽

Sidney Leibovich

Keyword(s):

Boundary Conditions ◽

Large Scale ◽

Evolution Equations ◽

Mixed Boundary ◽

Travelling Waves ◽

Temperature Fields ◽

Double Diffusive Convection ◽

Langmuir Circulation ◽

Diffusive Convection ◽

Double Diffusive

Two-dimensional Langmuir circulation in a layer of stably stratified water and the mathematically analogous problem of double-diffusive convection are studied with mixed boundary conditions. When the Biot numbers that occur in the mechanical boundary conditions are small and the destabilizing factors are large enough, the system will be unstable to perturbations of large horizontal length. The instability may be either direct or oscillatory depending on the control parameters. Evolution equations are derived here to account for both cases and for the transition between them. These evolution equations are not limited to small disturbances of the nonconvective basic velocity and temperature fields, provided the spatial variations in the horizontal remain small. The direct bifurcation may be supercritical or subcritical, while in the case of oscillatory motions, stable finite-amplitude travelling waves emerge. At the transition, travelling waves, standing waves, and modulated travelling waves all are stable in sub-regimes.

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Settling-driven large-scale instabilities in double-diffusive convection

Journal of Fluid Mechanics ◽

10.1017/jfm.2020.527 ◽

2020 ◽

Vol 901 ◽

Author(s):

Raphael Ouillon ◽

Philip Edel ◽

Pascale Garaud ◽

Eckart Meiburg

Keyword(s):

Large Scale ◽

Double Diffusive Convection ◽

Diffusive Convection ◽

Image Position ◽

Double Diffusive

Abstract

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Rotating double-diffusive convection in stably stratified planetary cores

Geophysical Journal International ◽

10.1093/gji/ggz347 ◽

2019 ◽

Vol 219 (Supplement_1) ◽

pp. S195-S218 ◽

Cited By ~ 1

Author(s):

R Monville ◽

J Vidal ◽

D Cébron ◽

N Schaeffer

Keyword(s):

Large Scale ◽

Critical Rayleigh Number ◽

Marginal Stability ◽

Early Earth ◽

Double Diffusive Convection ◽

Earth Core ◽

Diffusive Convection ◽

Non Linear ◽

Rayleigh Numbers ◽

Double Diffusive

SUMMARY In planetary fluid cores, the density depends on temperature and chemical composition, which diffuse at very different rates. This leads to various instabilities, bearing the name of double-diffusive convection (DDC). We investigate rotating DDC (RDDC) in fluid spheres. We use the Boussinesq approximation with homogeneous internal thermal and compositional source terms. We focus on the finger regime, in which the thermal gradient is stabilizing whereas the compositional one is destabilizing. First, we perform a global linear stability analysis in spheres. The critical Rayleigh numbers drastically drop for stably stratified fluids, yielding large-scale convective motions where local analyses predict stability. We evidence the inviscid nature of this large-scale double-diffusive instability, enabling the determination of the marginal stability curve at realistic planetary regimes. In particular, we show that in stably stratified spheres, the Rayleigh numbers Ra at the onset evolve like Ra ∼ Ek−1, where Ek is the Ekman number. This differs from rotating convection in unstably stratified spheres, for which Ra ∼ Ek−4/3. The domain of existence of inviscid convection thus increases as Ek−1/3. Secondly, we perform non-linear simulations. We find a transition between two regimes of RDDC, controlled by the strength of the stratification. Furthermore, far from the RDDC onset, we find a dominating equatorially antisymmetric, large-scale zonal flow slightly above the associated linear onset. Unexpectedly, a purely linear mechanism can explain this phenomenon, even far from the instability onset, yielding a symmetry breaking of the non-linear flow at saturation. For even stronger stable stratification, the flow becomes mainly equatorially symmetric and intense zonal jets develop. Finally, we apply our results to the early Earth core. Double diffusion can reduce the critical Rayleigh number by four decades for realistic core conditions. We suggest that the early Earth core was prone to turbulent RDDC, with large-scale zonal flows.

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