Dynamos in rotating compressible convection

流体磁发电机理论描述了由于导电流体的运动而产生的磁场的再生。发电机有许多物理例子，特别是在地球物理学和天体物理学中，发电机的作用在最近的液态金属实验室实验中被发现。热对流负责驱动这些天然发电机中的许多，其中绝大多数也依赖于旋转的动力影响。以前对旋转对流中发电机作用的大多数研究都采用了Boussinesq近似，这意味着(在其他方面)忽略了层化的影响。通过一系列的数值模拟，我们建议研究发电机在旋转可压缩对流中的作用，特别是层结对对流驱动的发电机的影响。具体地说，我们将讨论高度超临界可压缩对流中的发电机行为是否会导致大规模磁场的形成(这是同等的Boussinesq发电机无法做到的)。我们还将确定在弱-超临界参数区域(接近对流不稳定开始时)发电机行为是否存在最优旋转速度和最优层结水平。最后，受Boussinesq对流以前的结果的启发，我们将在亚临界参数区域寻找发电机作用，即在没有磁场的情况下不会发生对流不稳定的参数空间区域。

Hydromagnetic dynamo theory describes the regeneration of magnetic fields as the result of the motions of an electrically-conducting fluid. There are many physical examples of dynamos, particularly in geophysics and astrophysics, and dynamo action has been found in recent liquid metal laboratory experiments. Thermal convection is responsible for driving many of these natural dynamos, the vast majority of which also depend upon the dynamical influence of rotation. Most previous studies of dynamo action in rotating convection have adopted the Boussinesq approximation, which means (amongst other things) that the effects of stratification are ignored. By carrying out a series of numerical simulations, we propose to investigate dynamo action in rotating compressible convection, focusing particularly upon the effects that stratification has upon convectively-driven dynamos. Specifically, we shall address the question of whether or not dynamo action in highly-supercritical compressible convection can lead to the formation of large-scale magnetic fields (something that equivalent Boussinesq dynamos fail to do). We shall also establish whether there is an optimal rotation rate and an optimal level of stratification for dynamo action in the weakly-supercritical parameter regime (close to the onset of convective instabilities). Finally, motivated by previous results from Boussinesq convection, we will look for dynamo action in the subcritical parameter regime, i.e. a region of parameter space in which no convective instabilities would occur in the absence of a magnetic field.