Rossby waves and α-effect

Rossby waves drifting in the azimuthal direction are a common feature at the onset of thermal convective instability in a rapidly rotating spherical shell. They can also result from the destabilization of a Stewartson shear layer produced by differential rotation as expected in the liquid sodium experiment (Derviche Tourner Sodium) working in Grenoble, France. A usual way to explain why Rossby waves can contribute to the dynamo process goes back to Busse [A model of the Geodynamo. Geophys. J. R. Astron. Soc. 1975, 42, 437-459]. In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (parallel to the rotation axis) is maximum in the middle of each roll and changes its sign from one roll to the next (case (i)). It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an α-tensor with non-zero diagonal coefficients. It corresponds to the heuristic picture given by Busse (1975). In rapidly rotating objects like the Earth's core (or in a fast rotating experiment), Rossby waves occur in the limit of small Ekman number (≈[image omitted]). In that case, the main source of the axial flow component is not the Ekman pumping but rather the "geometrical slope effect" due to the spherical shape of the fluid containing shell. This implies that the axial flow component is maximum at the borders of the rolls and not at the centres (case (ii)). If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the α-tensor, making the dynamo probably less efficient if possible at all. Actually, the rolls are drifting as a wave, and we show that this drift implies non-zero coefficients on the diagonal of the α-tensor. These new coefficients are, in essence, very different from the ones obtained in case (i) and cannot be interpreted in terms of the heuristic picture of Busse (1975). They were interpreted as higher-order effects in Busse (1975). In addition, we consider rolls not only drifting but also having an arbitrary radial phase shift as expected in real objects.