Effects of Density Stratification on Convective Turbulence and Dynamo Action

太阳系中行星的磁场是由行星内部的湍流对流产生的。在这一过程的大多数数值模拟中，对流都是在Boussinesq近似的框架内模拟的。然而，通常情况下，在行星发电机区域，密度场随半径变化很大。这种背景密度变化对内部流动动力学有很大的影响，在Boussinesq模型中完全被忽略。我们计划在滞弹性框架中研究密度层化对湍流磁流体对流的影响，该框架过滤了声波引起的快速时间尺度。与简单的Boussinesq方法相比，滞弹性模型允许附加的动力学效应，如流体的膨胀和收缩，局部流体压缩对Taylor-Proudman定理的削弱，由独立于边界效应和磁浮力不稳定性的局部机制产生的平均流。与以尽可能接近地再现行星磁场的可观测特征为目标的全球模拟不同，我们的方法旨在研究全球区域小区域中的(磁)对流湍流的细节，从而将所有可用的计算资源引导到高度湍流状态的数值分辨率中。与以前在太阳能应用背景下进行的研究不同，我们将重点关注受自转强烈影响的流动。有条不紊地，我们将使用一种适用于大规模并行计算机的混合伪谱、有限差分代码。我们相信，拟议的工作将提供适用于类地行星、气体和冰巨星中的发电机以及快速旋转的恒星的新结果。

The magnetic fields of the planets in our solar system are generated by turbulent convective flows in the planetary interiors. In most numerical simulations of this process the convection is modelled in the framework of the Boussinesq approximation. Typically, the density field however varies considerably with radius in planetary dynamo regions. Such background density variations have a large impact on the interior flow dynamics and are completely neglected in Boussinesq models. We plan to study the effects of density stratification on turbulent magnetohydrodynamic convection in an anelastic framework which filters out fast time scales caused by sound waves. Compared to a simple Boussinesq approach, anelastic models allow for additional dynamical effects like fluid expansion and contraction, weakening of the Taylor-Proudman Theorem by local fluid compression, generation of mean flows by a local mechanism independent of boundary effects and magnetic buoyancy instabilities. In contrast to global simulations targeted at reproducing observable features of planetary magnetic fields as closely as possible, our approach is aimed at investigating the details of (magneto)-convective turbulence in small sub-sections of the global domain, thus channelling all available computational resources into the numerical resolution of highly turbulent states. Different from previous studies which have been carried out in the context of solar applications, we will focus on flows which are strongly influenced by rotation. Methodically, we will use a mixed pseudo-spectral, finite-difference code well adapted to massively parallel computers. We believe that the proposed work will provide new results applicable to dynamos in terrestrial planets, gas and ice giants as well as to rapidly rotating stars.