Abstract
We investigate incompressible, inviscid vorticity dynamics on a rotating unit sphere using a discrete exterior calculus scheme. For a prescribed initial vorticity distribution, we vary the rotation rate of the sphere from zero [non-rotating case, which corresponds to infinite Rossby number (Ro)] to 320 (which corresponds to Ro = 1.30 x 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. The energy cascades to the larger scales due to the inverse energy cascade, and at late times, an oscillating quadrupolar vortical field emerges. Rotation diminishes the forward cascade of enstrophy (and hence the inverse cascade of energy) and tends to align the vortical structures in the azimuthal/zonal direction. Our investigation reveals that, for the initial vorticity field comprising 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 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 for the parameter values employed in the present work.