The onset of thermo-compositional convection in rotating spherical shells

Abstract

Double-diffusive convection driven by both thermal and compositional buoyancy in a rotating spherical shell can exhibit a rather large number of behaviours often distinct from that of the single diffusive system. In order to understand how the differences in thermal and compositional molecular diffusivities determine the dynamics of thermo-compositional convection we investigate numerically the linear onset of convective instability in a double-diffusive setup. We construct an alternative equivalent formulation of the non-dimensional equations where the linearised double-diffusive problem is described by an effective Rayleigh number, $\text{Ra}$, measuring the amplitude of the combined buoyancy driving, and a second parameter, $\alpha$, measuring the mixing of the thermal and compositional contributions. This formulation is useful in that it allows for the analysis of several limiting cases and reveals dynamical similarities in the parameters space which are not obvious otherwise. We analyse the structure of the critical curves in this $\text{Ra}-\alpha$ space, explaining asymptotic behaviours in $\alpha$, transitions between inertial and diffusive regimes, and transitions between large scale (fast drift) and small scale (slow drift) convection. We perform this analysis for a variety of diffusivities, rotation rates and shell aspect ratios showing where and when new modes of convection take place.

arXiv commentAccepted for publication in Geophys. Astrophys. Fluid Dyn. on 2019-06-28 (Fist submitted on 2018-07-11). 24 pages, 10 figures

References in corpus (5)

• Thermal and electrical conductivity of iron at Earth's core conditions
• Parameter dependences of convection driven dynamos in rotating spherical fluid shells
• Patterns of convection in rotating spherical shells
• Inertial convection in rotating fluid spheres
• Double-diffusive convection in a rotating cylindrical annulus with conical caps

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• Fingering convection in the stably-stratified layers of planetary cores
• Effects of shell thickness on cross-helicity generation in convection-driven spherical dynamos
• Influence of Rotation on Fingering Convection in Planetary Cores
• Influence of Boundary Conditions and Heating Modes on the Onset of Columnar Convection in Rotating Spherical Shells