Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers

Most large-scale planetary magnetic fields are thought to be driven by low Rossby number convection of a low magnetic Prandtl number fluid. Here kinematic dynamo action is investigated with an asymptotic, rapidly rotating dynamo model for the plane layer geometry that is intrinsically low magnetic Prandtl number. The thermal Prandtl number and Rayleigh number are varied to illustrate fundamental changes in flow regime, ranging from laminar cellular convection to geostrophic turbulence in which an inverse energy cascade is present. A decrease in the efficiency of the convection to generate a dynamo, as determined by an increase in the critical magnetic Reynolds number, is observed as the buoyancy forcing is increased. This decreased efficiency may result from both the loss of correlations associated with the increasingly disordered states of flow that are generated, and boundary layer behavior that enhances magnetic diffusion locally. We find that the spatial characteristics of $\alpha$, and thus the large-scale magnetic field, is dependent only weakly on changes in flow behavior. However, our results are limited to the linear, kinematic dynamo regime, and future simulations including the Lorentz force are therefore necessary to assess the robustness of this result. In contrast to the large-scale magnetic field, the behavior of the small-scale magnetic field is directly dependent on, and therefore shows significant variations with, the small-scale convective flow field.

大多数大规模的行星磁场被认为是由低磁普朗特数流体的低罗斯比数对流驱动的。在此，利用一个渐近的、快速旋转的发电机模型对平面层几何结构（其本身具有低磁普朗特数）进行了运动学发电机作用的研究。改变热普朗特数和瑞利数以说明流态的基本变化，其范围从层状胞状对流到存在能量逆级串的地转湍流。随着浮力强迫的增加，观察到对流产生发电机的效率降低，这由临界磁雷诺数的增加所确定。这种效率降低可能是由于与所产生的日益无序的流态相关的相关性丧失，以及局部增强磁扩散的边界层行为所致。我们发现，$\alpha$的空间特性，进而大规模磁场，仅微弱地依赖于流态的变化。然而，我们的结果仅限于线性运动学发电机区域，因此未来包括洛伦兹力的模拟对于评估这一结果的稳健性是必要的。与大规模磁场相反，小规模磁场的行为直接依赖于小规模对流流场，因此随其有显著变化。