Double Diffusive Convection in Planetary Cores

双扩散对流(DDC)是一个术语，用来描述密度由两个组分组成的流体中产生的重力不稳定。这两个成分通常是温度(T)和成分(C)，这里我们假设高成分的区域比低成分的区域密度小(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，组成越高，密度越低)。这些不稳定性的出现依赖于流体密度的分层。分层必须是这样的：一个组件稳定地分层，而另一个则不稳定。这些不稳定性是由于这两个组分的扩散系数的大小不同造成的。这些不稳定性最初是在海洋学研究中发现的[1]，在那里人们发现有两种类型的DDC。首先，当密度的缓慢扩散分量(C)不稳定分层，而快速扩散分量(T)稳定时，发生指进对流。液团从高T/低C区向下的微小扰动将比其成分扩散的速度更快，因此，这个液团的密度比周围的流体更稠密，并将继续下降。其次，我们有振荡双扩散对流(ODDC)，它发生在快速扩散组分不稳定分层而缓慢扩散组分稳定的情况下。从两个流体层的界面向下扰动的流体块将加热到其周围环境的温度，然后向上上升到上面的区域，因为由于组成较高，它的密度低于周围的流体。当这个流体小团上升并进入低T/高C区域时，它将冷却并开始回落到高T/低C区域，在那里它将由于比以前更冷而进一步下沉，但组成上的差异将使该小块再次上升。这个过程会持续下去，并产生一个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，这一层可以极大地影响行星的磁场。为了更好地理解磁场中的波动，我们需要更深入地了解稳定顶层(STL)中的动力学。到目前为止，DDC已经在海洋学和天体物理学[2]中得到了研究，但关于它在行星核中的作用的研究很少[3，4]，因为对这些系统进行建模很困难。目前尚不清楚STL中的DDC如何影响磁场。本项目将侧重于ODDC，因为ODDC的起始范围在行星核特别宽(由于Prandtl数较低，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ODDC发生的参数区域；确定与ODDC相关的流动的大小和幅度，并评估旋转和球面几何形状对ODDC的影响。[1]M.E.斯特恩。盐泉与温盐对流。Tellus A，1960年。[2]J.S.特纳。多组分对流。《流体力学年报》，1985。[3]R.Monville，J.Vdal，D.Cebron和N.Schaeffer.稳定层结行星核中的旋转双扩散对流。《地球物理杂志国际》，2019年。[4]书名/作者声明：[by]A.水银堆芯双扩散对流发电机模型。《地球和行星科学通讯》，2010。[5]P.Garaud.低普朗特数下的双扩散对流。《流体力学年报》，2018。

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.