General problem of plasma turbulence can be formulated as advection of potential vorticity (PV), which handles flow self-organization, coupled to a number of other fields, whose gradients provide free energy sources. Therefore, focusing on PV evolution separates the underlying linear instability from the flow self-organization, and clarifies key spatial scales in terms of balances between various time scales. Considering the Hasegawa-Wakatani model as a minimal, nontrivial model of plasma turbulence where the energy is injected internally by a linear instability, we find that the critical wavenumber kc = C/κ where C is the adiabaticity parameter and κ is the normalized density gradient separates the adiabatic (or highly zonostrophic) behavior for large scales from the hydrodynamic behavior at small scales. In the adiabatic range the non-zonal part of the wave-number spectrum goes from

in the "inertial" range, where γ k and ω k are the linear growth and frequency and U is the rms zonal velocity. This proposed spectrum fits very well for the large kc case, where the bulk of the spectrum is in the adiabatic range. In contrast for small kc, we get the usual forward enstrophy cascade with

where ϵW is the enstrophy dissipation. In contrast for kc ≈ 1, the system transitions to hydrodynamic forward enstrophy cascade right after the injection range, with zonal flows at large scales and forward enstrophy cascade at small scales. Note that kc, can also be used as a proxy for the scale at which the system switches from wave-dominated (i.e. E (k) ∝ ω 2 k k -3 ) to hydrodynamic (i.e. E (k) ∝ ϵ 2/3 W k -3 ) spectra usually denoted by k β in geophysical fluid dynamics. It is argued that the ratio R β ≡ k β /k peak ≈ kc/k peak where k peak is the peak wave-number can be defined as the zonostrophy parameter, and that the abundance of zonal flows vs. eddies in near and far from "marginality" that is commonly formulated in terms of the Kubo number in plasma problems can also be understood in terms of the zonostrophy parameter, since R β increases as we approach marginality.