The nature of zonal jets in geostrophic turbulence

We examine different regimes obtained in forced-dissipative geostrophic turbulence on a midlatitude beta-plane. The regimes are obtained under different values of two length scales, (i) the usual Rhines scale associated with the total energy, and (ii) a length scale derived from the energy input rate and the background gradient of potential vorticity. Here we take advantage of the latest developments of the Contour-Advective Semi-Lagrangian algorithm to examine how the nature of the zonal jets emerging in this system depends crucially on the relative sizes of these two length scales. Although in all cases the turbulent mixing of potential vorticity tends to produce zonal jets, these vary considerably in their structure. Essentially, the number of jets obtained at equilibrium is broadly consistent with the Rhines scaling, whereas the sharpness of jets (suitably defined) depends on the second length scale associated with the forcing strength, which is here varied across several orders of magnitude. The regimes are characterized at strong forcing by zonal jets that remain indistinct, being continually disrupted by the energetic background turbulent flow, which contains strong eddy motions and coherent vortices. At small forcing, in contrast, zonal jets emerge with a clear potential vorticity staircase structure comprising near discontinuities in the zonal mean potential vorticity in the jet cores with perfectly mixed zones in between.

Further differences in jet structure are found to depend on the mechanism for energy input. A variety of forms have been used, from the traditional narrow-band, random-phase spectral forcing to broad-band coherent physical space forcing obtained through the injection of vortex dipoles. The above dependence of jet coherence on forcing strength is obtained in all cases. The uniformity of jet spacing, however, is found to be substantially greater for the narrow-band, random phase forcing than for the physical space forcing. Further, actual energy input rates measured in the simulations are also dependent on forcing mechanism, though in all cases are found to be significantly larger at small forcing than would be predicted on the basis of isotropic arguments, indicating strong eddy-jet correlations at the scales of the forcing.

Extensions to the analysis have been made to the case of finite Rossby deformation length and to the case of thermal-like energy dissipation, which is more effective at larger scales. The introduction of an extra length scale greatly enhances the variety of flow regimes obtained, with jets typically becoming increasingly undular at small deformation length. The analysis of these cases is further facilitated by the use of an equivalent latitude-type coordinate based on contours of potential vorticity that wrap the computational domain in the zonal direction.