http://arxiv.org/abs/1511.06164
The onset of dynamo action is investigated within the context of a newly developed low Rossby, low magnetic Prandtl number, convection-driven dynamo model. The model represents an asymptotically exact form of an $\alpha^2$ mean field dynamo model in which the small-scale convection is represented explicitly by the finite amplitude, single mode convective solutions first investigated by Bassom and Zhang (Geophys.~Astrophys.~Fluid Dyn., \textbf{76}, p.223, 1994). Both steady and oscillatory convection are considered for a variety of horizontal planforms. The kinematic helicity is observed to be a monotonically increasing function of the Rayleigh number; as a result, very small magnetic Prandtl number dynamos can be found for a sufficiently large Rayleigh number. All dynamos are found to be oscillatory with an oscillation frequency that increases as the strength of the convection is increased and the magnetic Prandtl number is reduced. Single mode solutions which exhibit boundary layer behavior in the kinematic helicity show a decrease in the efficiency of dynamo action due to the enhancement of magnetic diffusion in the boundary layer regions. For a given value of the Rayleigh number, lower magnetic Prandtl number dynamos are excited for the case of oscillatory convection in comparison to steady convection.
M. Calkins, K. Julien, S. Tobias, et. al.
Fri, 20 Nov 15
42/55
Comments: 13 pages, 12 figures