Small-scale dynamo action in rotating compressible convection

TL;DR

This study investigates how rotation and thermal stratification influence small-scale dynamo action in compressible convective flows, revealing that rotation lowers the critical magnetic Reynolds number and affects magnetic energy dissipation.

Contribution

It provides new insights into the effects of rotation and stratification on small-scale dynamo thresholds and saturation in compressible convection.

Findings

Rotation reduces the critical magnetic Reynolds number for dynamo action.

Thermal stratification has limited impact on the critical R_M in rotating cases.

Dynamo saturation levels are between 4% and 9% of kinetic energy.

Abstract

We study dynamo action in a convective layer of electrically-conducting, compressible fluid, rotating about the vertical axis. At the upper and lower bounding surfaces, perfectly-conducting boundary conditions are adopted for the magnetic field. Two different levels of thermal stratification are considered. If the magnetic diffusivity is sufficiently small, the convection acts as a small-scale dynamo. Using a definition for the magnetic Reynolds number $R_M$ that is based upon the horizontal integral scale and the horizontally-averaged velocity at the mid-layer of the domain, we find that rotation tends to reduce the critical value of $R_M$ above which dynamo action is observed. Increasing the level of thermal stratification within the layer does not significantly alter the critical value of $R_M$ in the rotating calculations, but it does lead to a reduction in this critical value in the non-rotating cases. At the highest computationally-accessible values of the magnetic Reynolds number, the saturation levels of the dynamo are similar in all cases, with the mean magnetic energy density somewhere between 4 and 9% of the mean kinetic energy density. To gain further insights into the differences between rotating and non-rotating convection, we quantify the stretching properties of each flow by measuring Lyapunov exponents. Away from the boundaries, the rate of stretching due to the flow is much less dependent upon depth in the rotating cases than it is in the corresponding non-rotating calculations. It is also shown that the effects of rotation significantly reduce the magnetic energy dissipation in the lower part of the layer. We also investigate certain aspects of the saturation mechanism of the dynamo.