Kinematic dynamo action in large magnetic Reynolds number flows driven by shear and convection

A numerical investigation is presented of kinematic dynamo action in a dyna mically driven fluid flow. The model isolates basic dynamo processes releva nt 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 J; the unit vectors (x) over cap, (y) over cap and (z) over cap point east, north and vertically upwards respectively. Relative to axes moving easterly with the local bulk motion of the fluid the rotation vector Omega lies in the (y,z)-plane inclined at an angle J to the z-axis, while the base of the layer moves with constant v elocity 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 la yer shear flow. The onset of instability is characterized by a horizontal w ave vector inclined at some angle e to the x-axis. Such motion is two-dimen sional, dependent only on two spatial coordinates together with time. It is supposed that this two-dimensionality persists into the various fully nonl inear regimes in which we study large magnetic Reynolds number kinematic dy namo action. When the Ekman layer flow is destabilized hydrodynamically, the fluid flow that results is steady in an appropriately chosen moving frame, and takes t he form of a row of cat's eyes. Kinematic magnetic field growth is characte rized by modes of two types. One is akin to the Ponomarenko dynamo mechanis m 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 con vective instability far from onset is characterized by a flow that is intri nsically time-dependent in the sense that it is unsteady in any moving fram e. The magnetic field is concentrated in magnetic sheets situated around th e convective cells in regions where chaotic particle paths are likely to ex ist; 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 laye r and localizes the magnetic field near the lower boundary.