On the problem of large-scale magnetic field generation in rotating compressible convection

TL;DR

This study investigates whether turbulent compressible convection in rotating layers can generate large-scale magnetic fields, finding that despite small-scale dynamo activity, large-scale field generation remains elusive even at high rotation rates.

Contribution

The paper extends previous Boussinesq models to compressible flows, demonstrating the persistent difficulty in achieving large-scale dynamo action in rapidly rotating turbulent convection.

Findings

Small-scale dynamo activity is observed in compressible rotating convection.

No significant large-scale magnetic field is generated even at high rotation rates.

Imposing a uniform magnetic field yields negligible alpha-effect in these simulations.

Abstract

Mean-field dynamo theory suggests that turbulent convection in a rotating layer of electrically-conducting fluid produces a significant alpha-effect, which is one of the key ingredients in any mean-field dynamo model. Provided that this alpha-effect operates more efficiently than (turbulent) magnetic diffusion, such a system should be capable of sustaining a large-scale dynamo. However, in the Boussinesq model that was considered by Cattaneo&Hughes (2006) the dynamo produced small-scale, intermittent magnetic fields with no significant large-scale component. In this paper, we consider the compressible analogue of the rotating convective layer that was considered by Cattaneo&Hughes (2006). Varying the horizontal scale of the computational domain, we investigate the dependence of the dynamo upon the rotation rate. Our simulations indicate that these turbulent compressible flows can drive a small-scale dynamo but, even when the layer is rotating very rapidly (with a mid-layer Taylor number of Ta=10^8), we find no evidence for the generation of a significant large-scale component of the magnetic field on a dynamical timescale. Like Cattaneo&Hughes(2006), we measure a negligible (time-averaged) alpha-effect when a uniform horizontal magnetic field is imposed across the computational domain. Although the total horizontal magnetic flux is a conserved quantity in these simulations, the (depth-dependent) horizontally-averaged magnetic field always exhibits strong fluctuations. If these fluctuations are artificially suppressed within the code, we measure a significant mean electromotive force that is comparable to that found in related calculations in which the alpha-effect is measured using the test-field method, even though we observe no large-scale dynamo action.