Two-Dimensional Turbulence and Persistent Zonal Jets in a Global Barotropic Model

Abstract

The dynamics of two-dimensional turbulence on a rotating sphere are examined. The anisotropic Rhines scale is derived and verified in decaying turbulence simulations. Due to the anisotropic nature of the Rossby waves, the Rhines barrier is displaced toward small total wavenumber n with decreasing zonal wavenumber m. Up-scale energy transfer along the zonal axis (m = 0) is not directly arrested by beta. A forced dissipative model with high-wavenumber forcing is used to investigate the dynamics of persistent zonal jets. Persistent jets form in the low energy (strong rotation) cases with the root-mean-square velocity V*rms ≪ aΩ. Under a fixed rotation rate, the jet scale decreases with the energy. The equilibrated jets generally stay at fixed latitudes. The zonal bands are nearly uniformly distributed in latitude, except that bands in the high latitudes tend to be wider and weaker, as clearly affected by a decreasing beta with latitude. The time-mean zonal winds in the forced simulations appear to be stable, with their absolute vorticity gradient dominated by beta. The increase of the jet scale with energy as required by stability is consistent with the simulated results. Diagnostic analysis shows that the persistent jets are primarily maintained by the shear-straining mechanism involving small-scale eddies and large-scale zonal jets, with a clear scale separation between them. Although large-scale eddies, those at scales near the Rhines scale, possess most of the eddy energy, in the time mean they contribute little to the maintenance of the zonal jets. Thus, despite the similarity between the Rhines scale and the jet scale, their dynamical link is not obvious in the time-mean statistics. The presence of persistent zonal jets modifies the normal modes of the system. Pure Rossby–Haurwitz modes at small and medium scales are severely modified and fall into the continuum. Large-scale modes, however, may remain discrete. The discreteness of the large-scale modes limits their ability to exchange energy with the zonal jets in the time mean.