Magnetic buoyancy instabilities in stellar interiors

磁浮力不稳定性可能发生在随深度变化的水平磁场中，这最终会出现，因为这样的场可以通过它施加的压力来支撑重气体。这些不稳定性已经在线性和非线性制度的研究了许多年。然而，许多未解决的问题仍然关于线性和非线性性质的不稳定性。最近，一组渐近简化的模型，这是更适合于计算和分析比完全可压缩系统，已经推导出描述磁浮力不稳定性在某些参数制度。磁浮力不稳定性的线性特性还没有被探索（在所有或全部）在这些模型中的几个以前。在这个项目中，我们将首先探讨磁浮力不稳定性的线性特性，在几个这些简化模型，然后再转向模拟其非线性演化。众所周知，在一定的参数制度磁浮力不稳定性是双扩散，和非线性演化可以导致分层的字段和密度分布。这些问题，以及由此产生的湍流传输特性，将探讨与数值模拟的目标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.