Barotropic Beta-Plane Turbulence in a Regime with Strong Zonal Jets Revisited

Abstract

The problem of quantification of barotropic beta-plane turbulence driven by small-scale stochastic forcing into regimes dominated by quasi-periodic zonal jets is revisited. It is shown that the large-scale relative vorticity in such regimes is organized into a sequence of zonal bands. Its zonal mean profile varies approximately linearly within the bands. Its mean negative slope ?? is less than the meridional gradient of the Coriolis parameter ?, and depends on the external parameters (friction, forcing, and ?). The neighboring bands are connected through the vorticity fronts where the zonal mean meridional gradient is large and positive. The frontal-band vorticity structure defines piecewise parabolic profiles of asymmetric eastward and westward jets, and strong peaks in the low-k interval of turbulent zonal energy spectra, which store most of the zonal energy. The slope of their envelope depends on the structure of the frontal zones and is always steeper than ?4. The presence of peaks invalidates the recent hypothesis on the universal power-law scaling Ez(k) = Cz?2k?5, Cz = O(1), for the zonal energy spectra of beta-plane turbulence in strongly anisotropic regimes. The power-law intervals could appear at large k and are linked to uncorrelated fluctuations of band profiles. It is shown that they could contain a part that slopes close to ?5. However, its Cz is not universal and depends on the external parameters. A simple kinematic model of multijet beta-plane flows is proposed that explains the shape of the coherent part of zonal energy spectra and asymmetry between westward and eastward jets generated by vorticity bands, and quantifies the zonal wavenumber of jets kj in terms of the ratio of zonal enstrophy to zonal energy.