Small-scale dynamo action in rotating compressible convection

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.

23 pages, 12 figures

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• Small-Scale Dynamo in Stably Stratified Turbulence
• Estimating the rate of field line braiding in the solar corona by photospheric flows
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• Analysis of scalar dissipation in terms of vorticity geometry in isotropic turbulence
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• On the saturation mechanism of the fluctuation dynamo at ${\text{Pr}}_{\mathrm{M}}\ge 1$
• Evolution and characteristics of forced shear flows in polytropic atmospheres: Large and small Péclet number regimes
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