Optimized kinematic dynamos

Growth rate degeneracies in kinematic dynamos.

We consider the classical problem of kinematic dynamo action in simple steady flows. Due to the adjointness of the induction operator, we show that the growth rate of the dynamo will be exactly the same for two types of magnetic boundary conditions: the magnetic field can be normal (infinite magnetic permeability, also called pseudovacuum) or tangent (perfect electrical conductor) to the bounda...

On Some Recent Results about Inertial Manifolds and Kinematic Dynamos

The conditions imposed in the paper [’Inertial manifolds and completeness of eigenmodes for unsteady magnetic dynamos’, Physica D 194 (2004) 297-319] on the fluid velocity to guarantee the existence of inertial manifolds for the kinematic dynamo problem are too demanding, in the sense that they imply that all the solutions tend exponentially to zero. The inertial manifolds are meaningful becaus...

Solar Interface Dynamos. I. Linear, Kinematic Models in Cartesian Geometry

We describe a simple, kinematic model for a dynamo operating in the vicinity of the interface between the convective and radiative portions of the solar interior. The model dynamo resides within a Cartesian domain, partioned into an upper, convective half and lower, radiative half, with the magnetic di†usivity g of the former region assumed to exceed that of the latter The Ñuid motions that con...

Topology and existence of 3D anisotropic filamentary kinematic dynamos

Curvature and helicity topological bounds for the magnetic energy of the streamlines magnetic structures of a kinematic dynamo flow are computed. The existence of the filament dynamos are determined by solving the magnetohydrodynamic equations for 3D flows and the solution is used to determine these bounds. It is shown that in the limit of zero resistivity filamentary dynamos always exists in t...

Optimized boundary driven flows for dynamos in a sphere