Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere

Abstract

Numerical solutions of the incompressible magnetohydrodynamic (MHD) equations are reported for the interior of a rotating, perfectly-conducting, rigid spherical shell that is insulator-coated on the inside. A previously-reported spectral method is used which relies on a Galerkin expansion in Chandrasekhar-Kendall vector eigenfunctions of the curl. The new ingredient in this set of computations is the rigid rotation of the sphere. After a few purely hydrodynamic examples are sampled (spin down, Ekman pumping, inertial waves), attention is focused on selective decay and the MHD dynamo problem. In dynamo runs, prescribed mechanical forcing excites a persistent velocity field, usually turbulent at modest Reynolds numbers, which in turn amplifies a small seed magnetic field that is introduced. A wide variety of dynamo activity is observed, all at unit magnetic Prandtl number. The code lacks the resolution to probe high Reynolds numbers, but nevertheless interesting dynamo regimes turn out to be plentiful in those parts of parameter space in which the code is accurate. The key control parameters seem to be mechanical and magnetic Reynolds numbers, the Rossby and Ekman numbers (which in our computations are varied mostly by varying the rate of rotation of the sphere) and the amount of mechanical helicity injected. Magnetic energy levels and magnetic dipole behavior are exhibited which fluctuate strongly on a time scale of a few eddy turnover times. These seem to stabilize as the rotation rate is increased until the limit of the code resolution is reached.

26 pages, 17 figures, submitted to New Journal of Physics

References in corpus (10)

• Astrophysical magnetic fields and nonlinear dynamo theory
• The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
• Magnetic Field Saturation in the Riga Dynamo Experiment
• Numerical study of dynamo action at low magnetic Prandtl numbers
• On the inverse cascade of magnetic helicity
• Observation of a Turbulence-Induced Large Scale Magnetic Field
• Direct simulations of helical Hall-MHD turbulence and dynamo action
• Magnetohydrodynamic activity inside a sphere
• Low magnetic Prandtl number dynamos with helical forcing
• Pressure determinations for incompressible fluids and magnetofluids

Cited by in corpus (7)

• Turbulent dynamos in spherical shell segments of varying geometrical extent
• On the emergence of very long time fluctuations and 1/f noise in ideal flows
• Magnetic field reversals and long-time memory in conducting flows
• The decay of magnetohydrodynamic turbulence in a confined domain
• Magnetic structure, dipole reversals, and 1/f noise in resistive MHD spherical dynamos
• Polarization properties of turbulent synchrotron bubbles: an approach based on Chandrasekhar-Kendall functions
• Behavior of hydrodynamic and magnetohydrodynamic turbulence in a rotating sphere with precession and dynamo action