Magnetic buoyancy instabilities in stellar interiors

随深度变化的水平磁场可能会出现磁浮力不稳定，这最终是因为这样的磁场可以通过其施加的压力来支持重气体。这些不稳定性已经在线性和非线性两种情况下进行了多年的研究。然而，关于不稳定性的线性和非线性性质，仍有许多未解决的问题。最近，一组较完全可压缩系统更易于计算和分析的渐近简化模型被推导出来，用于描述某些参数条件下的磁浮力不稳定性。磁性浮力不稳定性的线性特性在以前的几个模型中没有被探索（完全或完全）。在这个项目中，我们将首先探索这些简化模型中磁性浮力不稳定性的线性特性，然后再模拟它们的非线性演化。已知在某些参数条件下，磁浮力不稳定性是双扩散的，并且非线性演化会导致磁场和密度剖面的分层。这些问题，以及由此产生的湍流输运性质，将通过数值模拟来探索，目的是了解它们在恒星和行星内部的作用。

Magnetic buoyancy instabilities can occur for horizontal magnetic fields varying with depth, which ultimately arise because such a field can support a heavy gas by virtue of the pressure it exerts. These instabilities have been studied in both the linear and nonlinear regimes for a number of years. However, many unsolved problems remain regarding both the linear and nonlinear properties of the instability. Recently, a set of asymptotically-reduced models, that are more amenable to computation and analysis than the fully compressible system, have been derived that describe magnetic buoyancy instabilities in certain parameter regimes. The linear properties of magnetic buoyancy instabilities have not been explored (at all or fully) in several of these models previously. In this project we will first explore the linear properties of magnetic buoyancy instabilities in several of these reduced models, before turning to simulate their nonlinear evolution. It is known that in certain parameter regimes magnetic buoyancy instabilities are double-diffusive, and the nonlinear evolution can lead to layering in the field and density profiles. These issues, and the resulting turbulent transport properties, will be explored with numerical simulations with the goal of understanding their role in stellar and planetary interiors.