Double Diffusive Convection in Planetary Cores

双扩散对流（DDC）是一个用来描述重力不稳定性的术语，这种不稳定性出现在密度由两种成分组成的流体中。这两个组成部分通常是温度（T）和成分（C），在这里我们假设高成分区域的密度低于低成分区域（行星核心通常由液态铁组成，我们通过轻元素的浓度来测量成分）。因此，较高的组成导致较低的密度）。这些不稳定性的发生依赖于流体密度的分层。分层必须使得一个组分稳定分层，而另一个组分不稳定。这些不稳定性是由于这两种组分的扩散系数之间的大小差异而发生的。这些不稳定性最初是在海洋学研究中发现的[1]，其中发现有两种类型的DDC。首先，我们有指状对流，当密度的缓慢扩散分量（C）是不稳定的分层，而快速扩散分量（T）是稳定的。从高T/低C区域向下的流体包裹的无限小扰动将比其成分扩散更快地冷却，因此，该流体包裹比其周围的流体更致密，并且将继续下降。其次，我们有振荡的双扩散对流（ODDC），这发生在快速扩散的成分是不稳定的分层，而缓慢扩散的成分是稳定的。从两个流体层的界面向下扰动的流体包裹将升温到其周围的温度，然后上升回到上面的区域，因为它比周围的流体密度小，因为它的组成更高。当这个流体团上升并进入低T/高C区域时，它将冷却并开始回落到高T/低C区域，在那里由于它比以前更冷，它将进一步下沉，但成分的差异将再次驱动团回升。这一过程继续下去，并产生不稳定的内部重力波。为什么这与行星核心有关？在许多行星中，一个导电的、稳定分层的层被认为存在于产生行星磁场的发电机区域的正上方，这层可以极大地影响行星的磁场。为了更好地理解磁场的波动，我们需要更深入地了解稳定顶层（STL）的动态。到目前为止，DDC已经在海洋学和天体物理学中进行了研究[2]，但是很少有关于它在行星核心中的作用的研究[3，4]，因为模拟这些系统很困难。尚不清楚STL中的DDC如何影响磁场。该项目将重点关注ODDC，因为ODDC发生的范围在行星核心中特别宽（由于低普朗特数，即粘性耗散与热耗散之间的比率）[5]。我们将在没有磁场的情况下运行模拟，以便专注于流体的动力学。该项目的目的是确定发生ODDC的参数区域，确定与ODDC相关的流量的大小和幅度，并评估旋转和球形几何形状对ODDC的影响。[1] M.E.Stern.“盐泉”与温盐对流。Tellus A，1960年。[2] J.S.Turner.多组分对流流体力学年刊，1985. [3][1] J. J. J. Vidal，D.Cebron，& N. Schaiden.稳定分层行星核中的旋转双扩散对流。国际地球物理杂志，2019年。[4]题名/责任者：A. K. Manglik，J.Wicht，& U. R. Christensen.水星核心具有双扩散对流的发电机模型。地球和行星科学快报，2010年。[5] P.Garaud.低普朗特数下的双扩散对流。2018年流体力学年鉴

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.