A numerical investigation is presented of kinematic dynamo action in a dynamically
driven fluid flow. The model isolates basic dynamo processes relevant to field generation
in the Solar tachocline. The horizontal plane layer geometry adopted is chosen as
the local representation of a differentially rotating spherical fluid shell at co-latitude
ϑ; the unit vectors [xcirc ], ŷ and zˆ
point east, north and vertically upwards respectively.
Relative to axes moving easterly with the local bulk motion of the fluid the rotation
vector Ω lies in the (y, z)-plane inclined at an angle
ϑ to the z-axis, while the base of
the layer moves with constant velocity in the x-direction. An Ekman layer is formed
on the lower boundary characterized by a strong localized spiralling shear flow. This
basic state is destabilized by a convective instability through uniform heating at the
base of the layer, or by a purely hydrodynamic instability of the Ekman layer shear
flow. The onset of instability is characterized by a horizontal wave vector inclined at
some angle ∈ to the x-axis. Such motion is two-dimensional, dependent only on two
spatial coordinates together with time. It is supposed that this two-dimensionality
persists into the various fully nonlinear regimes in which we study large magnetic
Reynolds number kinematic dynamo action.
When the Ekman layer flow is destabilized hydrodynamically, the fluid flow that
results is steady in an appropriately chosen moving frame, and takes the form of a
row of cat's eyes. Kinematic magnetic field growth is characterized by modes of two
types. One is akin to the Ponomarenko dynamo mechanism and located close to some
closed stream surface; the other appears to be associated with stagnation points and
heteroclinic separatrices.
When the Ekman layer flow is destabilized thermally, the well-developed convective
instability far from onset is characterized by a flow that is intrinsically time-dependent
in the sense that it is unsteady in any moving frame. The magnetic field is concentrated
in magnetic sheets situated around the convective cells in regions where chaotic particle
paths are likely to exist; evidence for fast dynamo action is obtained. The presence
of the Ekman layer close to the bottom boundary breaks the up–down symmetry of
the layer and localizes the magnetic field near the lower boundary.