A Multiscale Dynamo Model Driven by Quasi-geostrophic Convection

Abstract

A convection-driven multiscale dynamo model is developed in the limit of low Rossby number for the plane layer geometry in which the gravity and rotation vectors are aligned. The small-scale fluctuating dynamics are described by a magnetically-modified quasi-geostrophic equation set, and the large-scale mean dynamics are governed by a diagnostic thermal wind balance. The model utilizes three timescales that respectively characterize the convective timescale, the large-scale magnetic evolution timescale, and the large-scale thermal evolution timescale. Distinct equations are derived for the cases of order one and low magnetic Prandtl number. It is shown that the low magnetic Prandtl number model is characterized by a magnetic to kinetic energy ratio that is asymptotically large, with ohmic dissipation dominating viscous dissipation on the large-scales. For the order one magnetic Prandtl number model the magnetic and kinetic energies are equipartitioned and both ohmic and viscous dissipation are weak on the large-scales; large-scale ohmic dissipation occurs in thin magnetic boundary layers adjacent to the solid boundaries. For both magnetic Prandtl number cases the Elsasser number is small since the Lorentz force does not enter the leading order force balance. The new models can be considered fully nonlinear, generalized versions of the dynamo model originally developed by Childress and Soward [Phys. Rev. Lett., \textbf{29}, p.837, 1972]. These models may be useful for understanding the dynamics of convection-driven dynamos in regimes that are only just becoming accessible to direct numerical simulations.

23 pages, 1 figure

References in corpus (3)

• Approaching the Asymptotic Regime of Rapidly Rotating Convection: Boundary Layers vs Interior Dynamics
• Generation of magnetic fields by large-scale vortices in rotating convection
• The Breakdown of the Anelastic Approximation in Rotating Compressible Convection: Implications for Astrophysical Systems

Cited by in corpus (27)

• Spherical convective dynamos in the rapidly rotating asymptotic regime
• The Turbulent Dynamo
• Approaching a realistic force balance in geodynamo simulations
• Approaching Earth's core conditions in high-resolution geodynamo simulations
• The interplay of fast waves and slow convection in geodynamo simulations nearing Earth's core conditions
• Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers
• Critical transition in fast-rotating turbulence within highly elongated domains
• Oscillatory thermal-inertial flows in liquid metal rotating convection
• Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: single mode solutions
• The Radius and Entropy of a Magnetized, Rotating Fully-convective Star: Analysis With Depth-dependent Mixing Length Theories
• Large-scale dynamos in rapidly rotating plane layer convection
• On the role of the Prandtl number in convection driven by heat sources and sinks
• Energy cascades in rapidly rotating and stratified turbulence within elongated domains
• Magnetic field generation by intermittent convection
• Fingering convection in the stably-stratified layers of planetary cores
• Equatorially Trapped Convection in a Rapidly Rotating Shallow Shell
• Inertia-less convectively-driven dynamo models in the limit of low Rossby number and large Prandtl number
• Direct numerical simulations of optimal thermal convection in rotating plane layer dynamos
• Strong large scale magnetic fields in rotating convection-driven dynamos: the important role of magnetic diffusion
• Asymptotic behaviour of rotating convection-driven dynamos in the plane layer geometry
• Effects of kinematic and magnetic boundary conditions on the dynamics of convection-driven plane layer dynamos
• Lorentz force mediation of turbulent dynamo transitions
• Turbulent 2.5 dimensional dynamos
• Magnetic quenching of the inverse cascade in rapidly rotating convective turbulence
• Efficiency gains of a multi-scale integration method applied to a scale-separated model for rapidly rotating dynamos
• Dynamo saturation down to vanishing viscosity: strong-field and inertial scaling regimes
• Non-equivalence of quasilinear dynamical systems and their statistical closures