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We investigate incompressible, inviscid vorticity dynamics on a rotating unitsphere using a Discrete Exterior Calculus (DEC) scheme. For a prescribedinitial vorticity distribution, we vary the rate of rotation of the sphere fromzero (non-rotating case, which corresponds to infinite Rossby number (Ro)) to320 (which corresponds to Ro = $1.30 \times 10^{-3}$), and investigate theevolution with time of the vorticity field. For the non-rotating case, thevortices evolve into thin filaments due to so-called forward/direct enstrophycascade. At late times an oscillating quadrupolar vortical field emerges as aresult of the inverse energy cascade. Rotation diminishes the forward cascadeof enstrophy (and hence the inverse cascade of energy) and tend to align thevortical structures in the azimuthal/zonal direction. Our investigation revealsthat, for the initial vorticity field comprising of intermediate-wavenumberspherical harmonics, the zonalization of the vortical structures is notmonotonic with ever decreasing Rossby numbers and the structures revert back toa non-zonal state below a certain Rossby number. On the other hand, for theinitial vorticity field comprising of intermediate to large-wavenumberspherical harmonics, the zonalization is monotonic with decreasing Rossbynumber. Although, rotation diminishes the forward cascade of enstrophy, it doesnot completely cease/arrest the cascade.

Effects of Rotation on Vorticity Dynamics on a Sphere with Discrete Exterior Calculus