Application of a simple diffusivity formation to examine regime transition and jet-eddy energy partitioning in quasi-geostrophic turbulence

Abstract

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 (Df) in the limit of vanishing β (termed drag-controlled) while reduced to a drag-independent scaling (Dβ) of Lapeyre and Held (2003) toward large β (termed β-controlled). Good agreement is found for diffusivities diagnosed from simulations with both quadratic and linear drag and in 2D turbulence. From the formulation, a regime diagram is readily constructed, with Df /Dβ = 1 separating the drag- and β-controlled regimes. The diagram also sets the parameter range where an eddy velocity scaling is applicable. 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, using Df /Dβ ≥ 10, a state where eddy statistics are approximately drag insensitive could be identified and interpreted using wave-damping competitions in slowing an inverse cascade. 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.