Anisotropic -5/3 and -5 Spectra in Differentially Rotating Barotropic 2D Turbulence

Differential rotation effects the large scale dynamics of small scale forced, 2D turbulence via reorganization of the spectrum from the Kolmogorov -5/3 to -5 law (Rhines, 1975). This prediction was corroborated in simulations by Sukoriansky et al. (1996) in a periodic box setting on β-plane. It was shown that on the large scales, the energy transfer develops strong spectral anisotropy preferring the modes with kx → 0 that correspond to zonal jets. The spectrum also undergoes anisotropization whereas -5/3 law prevails for all directions except for a small sector kx → 0 where -5 law dominates. Here, we further corroborate these results in simulations of barotropic 2D turbulence on the surface of a rotating sphere. Specifically, it is shown that the large scale spectrum develops strong anisotropy fully consistent with the β-plane simulations. These results may have important implications for long term climate change related computations.