  We investigate incompressible, inviscid vorticity dynamics on a rotating unit
sphere using a Discrete Exterior Calculus (DEC) scheme. For a prescribed
initial vorticity distribution, we vary the rate of rotation of the sphere from
zero (non-rotating case, which corresponds to infinite Rossby number (Ro)) to
320 (which corresponds to Ro = $1.30 \times 10^{-3}$), and investigate the
evolution with time of the vorticity field. For the non-rotating case, the
vortices evolve into thin filaments due to so-called forward/direct enstrophy
cascade. At late times an oscillating quadrupolar vortical field emerges as a
result of the inverse energy cascade. Rotation diminishes the forward cascade
of enstrophy (and hence the inverse cascade of energy) and tend to align the
vortical structures in the azimuthal/zonal direction. Our investigation reveals
that, for the initial vorticity field comprising of intermediate-wavenumber
spherical harmonics, the zonalization of the vortical structures is not
monotonic with ever decreasing Rossby numbers and the structures revert back to
a non-zonal state below a certain Rossby number. On the other hand, for the
initial vorticity field comprising of intermediate to large-wavenumber
spherical harmonics, the zonalization is monotonic with decreasing Rossby
number. Although, rotation diminishes the forward cascade of enstrophy, it does
not completely cease/arrest the cascade.
