Open and closed boundaries in large-scale convective dynamos

Abstract

Context. Earlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. Aims. Our aim is to test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Methods. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation of large-scale dynamos. Open (vertical-field) and closed (perfect-conductor) boundary conditions are used for the magnetic field. The shear flow is such that the contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. Results. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate of the field in this regime increases as Rm^(1/2). Regarding the nonlinear regime, the saturation level of the energy of the total magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.

9 pages, 7 figures, published version

References in corpus (8)

• The case for a distributed solar dynamo shaped by near-surface shear
• Large-scale dynamos in turbulent convection with shear
• Alpha effect and turbulent diffusion from convection
• Minimal tau approximation and simulations of the alpha effect
• Small-scale magnetic helicity losses from a mean-field dynamo
• Effects of fluctuation on alpha-omega dynamo models
• Catastrophic alpha quenching alleviated by helicity flux and shear
• The alpha effect in rotating convection with sinusoidal shear

Cited by in corpus (20)

• Dynamo theories
• The Wisconsin Plasma Astrophysics Laboratory
• The subsurface-shear shaped solar $\alpha \Omega$ dynamo
• Magnetorotational instability driven dynamos at low magnetic Prandtl numbers
• Turbulent dynamo with advective magnetic helicity flux
• Convection-driven spherical shell dynamos at varying Prandtl numbers
• Dynamo action and magnetic buoyancy in convection simulations with vertical shear
• Gravitoturbulent dynamos in astrophysical discs
• Magnetic helicity flux in the presence of shear
• Small-scale dynamo action in rotating compressible convection
• Spherical-shell boundaries for two-dimensional compressible convection in a star
• On the problem of large-scale magnetic field generation in rotating compressible convection
• Oscillatory large-scale dynamos from Cartesian convection simulations
• Magnetic Clouds: Solar Cycle Dependence, Sources, and Geomagnetic Impacts
• Accretion Disks and Dynamos: Toward a Unified Mean Field Theory
• Turbulent magnetic helicity fluxes in solar convective zone
• On global solar dynamo simulations
• MRI turbulence in vertically stratified accretion discs at large magnetic Prandtl numbers
• Budget equations and astrophysical nonlinear mean-field dynamos
• Constraining the outer boundary condition for the Babcock-Leighton dynamo models