Zonal jets and eddy tilts in barotropic geostrophic turbulence

The spontaneous formation of zonal jets is a distinctive feature of geostrophic turbulence with the phenomenon witnessed in numerous numerical studies. In such systems, strong rotation anisotropises the spectral evolution of the energy density such that zonal modes are favoured. In physical space, this manifests as eddies zonally elongating and forming into zonal jets. In the presence of large scale dissipation, the flow may reach statistical stationarity such that the zonal structure persists in the zonal and time mean, and is supported by a flux of eddy momentum. What is unclear is how the excitation of Rossby waves arranges the underlying eddy momentum stresses to support the mean flow structures. To study this, we examine a steady-state flow in the so-called ‘zonostrophic’ regime, in which characteristic scales of geostrophic turbulence are well separated and there are several alternating zonal jets that have formed spontaneously. We apply a geometric eddy ellipse formulation, in which momentum fluxes are cast as ellipses that encode information about the magnitude and direction of flux; the latter is described using the tilt angle. With the aid of a zonal filter, it is revealed that the scales responsible for providing the momentum fluxes associated with the jet structure are much smaller than the characteristic scales identified, and occupy a region of the energy spectrum that has been typically associated with isotropic dynamics.