Convection-driven kinematic dynamos with a self-consistent shear flow

ABSTRACT It is widely accepted that astrophysical magnetic fields are generated by dynamo action. In many cases, these fields exhibit organisation on a scale larger than that of the underlying turbulent flow (e.g. the 11-year solar cycle). The mechanism for the generation of so-called large-scale fields remains an open problem. In cases where the magnetic Reynolds number (Rm) is small, dynamo-generated fields are coherent but at (the astrophysically relevant) high Rm, the fields are overwhelmed by small-scale fluctuating field. Recently Tobias and Cattaneo have shown that an imposed large-scale shear flow can suppress the small-scale fluctuations and allow the large-scale temporal behaviour to emerge. Shear is also believed to modify the electromotive force by introducing correlations between the flow and the field. However, in previous models at high Rm the shear is often artificially imposed or driven by an arbitrary body force. Here we consider a simple kinematic model of a convective dynamo in which shear is self-consistently driven by the presence of a horizontal temperature gradient (resulting in a thermal wind) and a rotation vector that is oblique to gravity. By considering a -dimensional system, we are able to reach high Rm so that the dynamo approaches the asymptotic regime where the growth rate becomes approximately independent of Rm. We find the flows studied here to be excellent small-scale dynamos, but with very little systematic behaviour evident at large Rm. We attribute this to being unable to self-consistently generate flows with both large (net) helicity and strong shear in this setup.

**摘要**：天体物理磁场由发电机作用产生，这一观点已被广泛接受。在许多情况下，这些磁场呈现出的组织规模大于其下的湍流尺度（例如11年的太阳活动周期）。所谓大尺度磁场的产生机制仍然是一个未解决的问题。在磁雷诺数（Rm）较小的情况下，发电机产生的磁场是相干的，但在（与天体物理相关的）高Rm时，磁场被小尺度的涨落场淹没。最近，托拜厄斯和卡塔内奥表明，施加的大尺度剪切流能够抑制小尺度涨落，并使大尺度的时间行为显现出来。人们还认为，剪切通过引入流场和磁场之间的相关性来改变电动势。然而，在先前高Rm的模型中，剪切通常是人为施加的，或者是由任意体力驱动的。在这里，我们考虑一个对流发电机的简单运动学模型，其中剪切是由水平温度梯度（导致热成风）和一个与重力方向倾斜的旋转矢量的存在自洽地驱动的。通过考虑一个二维系统，我们能够达到高Rm，使得发电机接近渐近状态，此时增长率变得近似与Rm无关。我们发现这里所研究的流是很好的小尺度发电机，但在高Rm时几乎没有明显的系统性行为。我们将此归因于在这种设置下无法自洽地产生同时具有大（净）螺旋度和强剪切的流。