Double Diffusive Convection in Planetary Cores

Double-diffusive convection (DDC) is a term used to describe gravitational instabilities that arise within a fluid whose density is made up of two components. These two components are usually temperature (T) and composition (C), where here we will assume the region of high composition is less dense than a region of lower composition (planetary cores are usually comprised of liquid iron and we measure the composition by the concentration of light elements. Thus, higher composition leads to lower density). The onset of these instabilities rely on the stratification of the fluid's density. The stratification must be such that one component is stably stratified while the other is not. These instabilities occur as a result of the difference in size between the diffusion coefficients of these two components. The initial discovery of these instabilities was in the study of oceanography [1], where it was found that there are two types of DDC. Firstly, we have fingering convection which occurs when the slowly diffusing component (C) of the density is unstably stratified while the rapidly diffusing component (T) is stable. An infinitesimal perturbation of a fluid parcel downwards from the high-T/low-C region will cool faster than its composition can diffuse, thus, this fluid parcel is denser than the fluid surrounding it and will continue to fall. Secondly, we have oscillatory double diffusive convection (ODDC), which occurs when the rapidly diffusing component is unstably stratified while the slowly diffusing component is stable. A fluid parcel perturbed downward from the interface of the two fluid layers will warm to the temperature of its surroundings, then ascend back up into the region above as it is less dense than the fluid around it due to the higher composition. As this fluid parcel rises and enters the low-T/high-C region, it will cool and begin to fall back into the high-T/low-C region where it will sink further due to it being cooler than before, but the difference in composition will drive the parcel back up again. This process continues and creates an unstable internal gravity wave.

Why is this relevant to planetary cores? In many planets, an electrically-conducting, stably-stratified layer is thought to be present immediately above the dynamo region where the planet's magnetic field is generated, this layer can vastly affect the magnetic field of the planet. To better understand fluctuations in the magnetic field we need a deeper insight into the dynamics in the stable top layer (STL). Thus far DDC has been studied in oceanography and astrophysics [2], yet there are few studies regarding its role in planetary cores [3,4] as modelling these systems is difficult. It is unknown how DDC in the STL may influence magnetic fields. This project will focus on ODDC as the range at which the onset of ODDC occurs is particularly wide in planetary cores (due to the low Prandtl number, that is the ratio between viscous dissipation to thermal dissipation) [5]. We will be running the simulations in the absence of a magnetic field, in order to focus on the fluid's dynamics. The aims for this project are to identify the parameter region in which ODDC occurs; determine the size and amplitude of flows associated with ODDC and assess the effect of both rotation and spherical geometry on ODDC.

[1] M.E.Stern. The "salt-fountain" and thermohaline convection. Tellus A,1960.
[2] J.S.Turner. Multicomponent convection. Annual Review of Fluid Mechanics,1985.
[3] R.Monville, J.Vidal, D.Cebron, & N.Schaeffer. Rotating double-diffusive convection in stably stratified planetary cores. Geophysical Journal International, 2019.
[4] A.K.Manglik, J.Wicht, & U.R.Christensen. A dynamo model with double diffusive convection for mercury's core. Earth and Planetary Science Letters,2010.
[5] P.Garaud. Double-diffusive convection at low prandtl number. Annual Review of Fluid Mechanics,2018.