Drag & beta both at play 

Can we estimate the strength of zonal jets emerged from geostrophic turbulence? What is the energy partitioning between eddies and jets?

This study uses a simple diffusivity formulation to examine flow regime transition and jet–eddy energy partitioning in two-layer quasi-geostrophic turbulence. Guided by simulations, the formulation is empirically constructed so that the diffusivity is bounded by a f-plane asymptote in the limit of vanishing beta (termed drag-controlled) while reduced to a drag- independent scaling of Lapeyre and Held toward large beta (termed beta-controlled). Good agreement is found for diffusivities diagnosed from simulations with both quadratic and linear drag and in 2D turbulence. The quantitative representations of eddy variables then enable a reasonably skillful theory for zonal jet speed to be developed from energy balance. It is shown that a state where eddy statistics are approximately drag insensitive could indeed be identified. However, contrary to an existing hypothesis, the energy dissipation in such a state is not dominated by zonal jets. A modest revision for a way to maintain balance while keeping eddies drag insensitive is proposed. In the regime diagram, a subspace of zonostrophic condition, defined as jet dissipation surpassing eddy, is further quantified. It is demonstrated that a rough scaling could help interpret how the relative importance of jet and eddy dissipation varies across the parameter space.

Ref:  Chen, S. N., 2024: Application of a simple diffusivity formulation to examine regime transition and jet-eddy energy partitioning in quasi-geostrophic turbulence. Journal of Physical Oceanography, 54, 557-576.