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A numerical investigation of convection-driven dynamos is carried out in the plane layer geometry. Dynamos with different magnetic Prandtl numbers Pm are simulated over a broad range of the Rayleigh number Ra. The heat transport, as characterized by the Nusselt number Nu, shows an initial departure from the heat transport scaling of non-magnetic Rayleigh-Bénard convection (RBC) as the magnetic field grows in magnitude; as Ra is increased further, the data suggest that Nu grows approximately as Ra2/7, but with a smaller prefactor in comparison with RBC. Viscous (u) and ohmic (B) dissipation contribute approximately equally to Nu at the highest Ra investigated; both ohmic and viscous dissipation approach a Reynolds-number-dependent scaling of the form Rea, where a ≈ 2.8. The ratio of magnetic to kinetic energy approaches a Pm-dependent constant as Ra is increased, with the constant value increasing with Pm. The ohmic dissipation length scale depends on Ra in such a way that it is always smaller, and decreases more rapidly with increasing Ra, than the viscous dissipation length scale for all investigated values of Pm. [ABSTRACT FROM AUTHOR]

The relationship between nonlinear large-scale dynamo action and the generation and transport of magnetic helicity is investigated at moderate values of the magnetic Reynolds number ($Rm$). The model consists of a helically forced, sheared flow in a Cartesian domain. The boundary conditions are periodic in the horizontal and impenetrable for the vertical. The magnetic field is required to be vertical at the upper and lower boundaries. There are two consequences of this choice; one is that the magnetic helicity is not gauge invariant, the second is that fluxes of magnetic helicity are allowed in and out of the domain. We select the winding gauge, define all the contributions to the evolution of the helicity in this gauge and measure these contributions for various solutions of the dynamo equations. We vary $Rm$ and the shear strength, and find a rich landscape of dynamo solutions including travelling waves, pulsating waves and non-wave-like solutions. We find that, at the $Rm$ considered, the main contribution to the growth of magnetic helicity comes from processes throughout the volume of the fluid and that boundary terms respond by limiting the growth. We find that, in this magnetic Reynolds number regime, helicity conservation is not a strong constraint on large-scale dynamo action. We speculate on what may happen at higher $Rm$. [ABSTRACT FROM AUTHOR]

We consider kinematic dynamo action in a sheared helical flow at moderate to high values of the magnetic Reynolds number (Rm). We find exponentially growing solutions which, for large enough shear, take the form of a coherent part embedded in incoherent fluctuations. We argue that at large Rm large-scale dynamo action should be identified by the presence of structures coherent in time, rather than those at large spatial scales. We further argue that although the growth rate is determined by small-scale processes, the period of the coherent structures is set by mean-field considerations. [ABSTRACT FROM AUTHOR]

In an earlier paper [P. W. Livermore, D. W. Hughes, and S. M. Tobias, “The role of helicity and stretching in forced kinematic dynamos in a spherical shell,” Phys. Fluids 19, 057101 (2007)], we considered the kinematic dynamo action resulting from a forced helical flow in a spherical shell. Although mean field electrodynamics suggests that the resulting magnetic field should have a significant mean (axisymmetric) component, we found no evidence for this; the dynamo action was distinctly small scale. Here we extend our investigation into the nonlinear regime in which the magnetic field reacts back on the velocity via the Lorentz force. Our main result is somewhat surprising, namely, that nonlinear effects lead to a considerable change in the structure of the magnetic field, its final state having a significant mean component. By investigating the dominant flow-field interactions, we isolate the dynamo mechanism and show schematically how the generation process differs between the kinematic and nonlinear regimes. In addition, we are able to calculate some components of the transport coefficient α and thus discuss our results within the context of mean field electrodynamics. [ABSTRACT FROM AUTHOR]

The operation of an interface dynamo (as has been suggested for the Sun and other stars with convective envelopes) relies crucially upon the effective transport of magnetic flux between two spatially disjoint generation regions. In the simplest models communication between the two regions is achieved solely by diffusion. Here we incorporate a highly simplified anisotropic transport mechanism in order to model the net effect of flux conveyance by magnetic pumping and by magnetic buoyancy. We investigate the influence of this mechanism on the efficiency of kinematic dynamo action. It is found that the effect of flux transport on the efficiency of the dynamo is dependent upon the spatial profile of the transport. Typically, transport hinders the onset of dynamo action and increases the frequency of the dynamo waves. However, in certain cases, there exists a preferred magnitude of transport for which dynamo action is most efficient. Furthermore, we demonstrate the importance of the imposition of boundary conditions in drawing conclusions on the role of transport. [ABSTRACT FROM AUTHOR]

Considerations of mean-field theory suggest that small-scale helical flows are an effective means of generating large-scale (mean) magnetic fields, whereas fast dynamo considerations reveal the importance of Lagrangian chaos in the flow for generating small-scale magnetic fields in the limit of high magnetic Reynolds number. We explore these ideas further by considering the kinematic magnetic fields generated by three forced steady flows in a spherical shell that differ both in their helicity and in their stretching properties. The full magnetic induction equation is solved numerically, with no a priori assumptions about the nature of the generated magnetic field. There are two surprising aspects to our results. One is that the most significant mean field is generated by a flow with zero net helicity; the other is that the flow with the “best” stretching properties turns out to be the most inefficient dynamo. Our results, therefore, suggest that it may not be possible to determine the nature of a kinematic-dynamo generated magnetic field simply from the knowledge of certain flow properties. [ABSTRACT FROM AUTHOR]