Dynamos in rotating compressible convection

磁流体发电机理论描述了由于导电流体的运动而产生的磁场再生。发电机有许多物理例子，特别是在天体物理学和天体物理学中，最近的液态金属实验室实验中发现了发电机作用。热对流是驱动许多这些自然发电机的原因，其中绝大多数还取决于旋转的动力学影响。以前大多数关于旋转对流发电机作用的研究都采用了Boussinesq近似，这意味着忽略了层结的影响。通过进行一系列的数值模拟，我们建议调查发电机在旋转可压缩对流的行动，特别是侧重于对流驱动发电机分层后的影响。具体地说，我们将解决的问题，发电机行动在高度超临界可压缩对流是否可以导致大规模磁场的形成（等效Boussinesq发电机未能做到这一点）。我们还将建立是否有一个最佳的旋转速率和分层发电机行动的最佳水平在弱超临界参数制度（接近对流不稳定性的发病）。最后，受Boussinesq对流先前结果的启发，我们将在亚临界参数范围内寻找发电机作用，即在没有磁场的情况下不会发生对流不稳定性的参数空间区域。

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.