Zonal current formation in two-dimensional turbulence on a rotating hemisphere and its dependence on boundary conditions

Flow pattern of two-dimensional decaying incompressible turbulence is studied numerically on a rotating hemisphere with the rigid/stress-free boundary at the equator. A stereographic projection of the hemisphere to a plane disk, followed by Fourier-Chebyshev expansion method, is employed for the numerical calculation. It is observed that an eastward flow is formed in the rigid-boundary case, while a westward flow in the stress-free-boundary case, from randomized initial conditions.