Rossby waves and $\alpha$-effect

TL;DR

This paper investigates Rossby waves in rapidly rotating spherical shells and their role in dynamo processes, highlighting how wave drift influences the $oldsymbol{ ext{α}}$-effect tensor coefficients.

Contribution

It reveals that Rossby wave drift induces non-zero diagonal $oldsymbol{ ext{α}}$-tensor coefficients, challenging previous stationary flow assumptions and providing new insights into dynamo mechanisms.

Findings

Rossby wave drift leads to non-zero $oldsymbol{ ext{α}}$-tensor diagonal coefficients.

Geometrical slope effect dominates axial flow in Earth's core-like conditions.

Drifting Rossby waves alter the classical dynamo interpretation based on stationary flows.

Abstract

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 (DTS) working in Grenoble, France. A usual way to explain why Rossby waves can participate to the dynamo process goes back to Busse (1975). In his picture, the flow geometry is a cylindrical array of parallel rolls aligned with the rotation axis. The axial flow component (the component parallel to the rotation axis) is (i) maximum in the middle of each roll and changes its sign from one roll to the next. It is produced by the Ekman pumping at the fluid containing shell boundary. The corresponding dynamo mechanism can be explained in terms of an $\alpha$-tensor with non-zero coefficients on the diagonal. 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 ($\approx 10^{-15}$). 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 (ii) maximum at the borders of the rolls and not at the centers. If assumed to be stationary, such rolls would lead to zero coefficients on the diagonal of the $\alpha$-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 $\alpha$-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).