Helicity segregation by Ekman pumping in laminar rotating flows with gravity orthogonal to the rotation

Kinetic helicity in most geodynamo simulations has a distinct distribution above and below the equator -- it is negative in the north and positive in the south. Using direct numerical simulations of rotating convection, with the rotation axis perpendicular to gravity, we investigate the role of Ekman pumping as a possible mechanism behind this helicity segregation. For a fixed Rayleigh number $Ra=10^5$ and Prandtl number $Pr=1$, we consider two values of Taylor number, $Ta=10^5$ and $10^6$, and two different boundary conditions -- no-slip and fixed stress at the walls normal to the rotation axis.

We observe cyclonic flow in bulk and helical flow driven by Ekman pumping near the boundaries normal to the rotation axis. This leads to helicity being negative (positive) near the wall with outward normal parallel (anti-parallel) to the rotation vector. The peak in helicity (averaged in the plane normal to the rotation axis) occurs inside the Ekman layer in all simulations. The helicity magnitude is smaller for the fixed stress boundary condition as compared to no-slip. We also observe that the buoyancy causes the large helicity regions inside the Ekman boundary layer to migrate away from the rotation axis. We also present the helicity budget analysis, with the contribution of Coriolis force, pressure-vorticity, buoyancy force, and viscosity in the helicity segregation. We find that both pressure-vorticity and Coriolis forces contribute significantly to the helicity segregation. Moreover, from modal energy analysis, we find that the mode (2, 2), which represents the secondary flows, is important for helicity segregation.