Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry

Abstract

Dynamos driven by rotating convection in the plane layer geometry are investigated numerically for a range of Ekman number ($E$), magnetic Prandtl number ($Pm$) and Rayleigh number ($Ra$). The primary purpose of the investigation is to compare results of the simulations with previously developed asymptotic theory that is applicable in the limit of rapid rotation. We find that all of the simulations are in the quasi-geostrophic regime in which the Coriolis and pressure gradient forces are approximately balanced at leading order, whereas all other forces, including the Lorentz force, act as perturbations. Agreement between simulation output and asymptotic scalings for the energetics, flow speeds, magnetic field amplitude and length scales is found. The transition from large scale dynamos to small scale dynamos is well described by the magnetic Reynolds number based on the small convective length scale, $\widetilde{Rm}$, with large scale dynamos preferred when $\widetilde{Rm}\lesssim O(1)$. The magnitude of the large scale magnetic field is observed to saturate and become approximately constant with increasing Rayleigh number. Energy spectra show that all length scales present in the flow field and the small-scale magnetic field are consistent with a scaling of $E^{1/3}$, even in the turbulent regime. For a fixed value of $E$, we find that the viscous dissipation length scale is approximately constant over a broad range of $Ra$; the ohmic dissipation length scale is approximately constant within the large scale dynamo regime, but transitions to a ${\widetilde{Rm}}^{-1/2}$ scaling in the small scale dynamo regime.

38 pages, 13 figures

References in corpus (11)

• Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics
• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• Large-scale vortices in rapidly rotating Rayleigh-Bénard convection
• Approaching a realistic force balance in geodynamo simulations
• The effects of Ekman pumping on quasi-geostrophic Rayleigh-Benard convection
• Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers
• Relating force balances and flow length scales in geodynamo simulations
• Velocimetry in rapidly rotating convection: spatial correlations, flow structures and length scales
• Large-scale-vortex dynamos in planar rotating convection
• Magnetic energy dissipation and mean magnetic field generation in planar convection driven dynamos
• Strong large scale magnetic fields in rotating convection-driven dynamos: the important role of magnetic diffusion

Cited by in corpus (5)

• Reynolds number scaling and energy spectra in geostrophic convection
• Effects of kinematic and magnetic boundary conditions on the dynamics of convection-driven plane layer dynamos
• Small-scale and large-scale dynamos in global convection simulations of solar-like stars
• Dynamic regimes in planetary cores: τ-{\ell} diagrams
• Transition to chaos and magnetic field generation in rotating Rayleigh-Bénard convection