What Limits Zonal Flow Saturation in (Nearly) Collisionless Drift-Wave Turbulence?*

Drift wave - zonal flow turbulence has long been known as a self-regulating system. A key question that remains is how are zonal shears regulated with weak frictional damping. 

For realistic values of electron adiabaticity in the Hasegawa-Wakatani model, Rayleigh-Kuo can be used as a stability criterion. Rayleigh-Kuo states that for zonal flow stability to occur, it is necessary for the total mean potential vorticity gradient to vanish, i.e. ∇(PV) = ∇( - ∇²<??>) = 0. We explore the relation between this criterion and saturated turbulence levels through the quantity R = Zonal Flow Energy / Drift Wave Energy with varying levels of frictional damping (??) and frozen ∇(). Here, “zonal” means k_?? and k_z = 0 and “drift wave” means k_?? and k_z ≠ 0. 

Current results show that lower damping scenarios are consistent with Rayleigh-Kuo with R < 1 regions centralized around ∇(PV) = 0. Larger damping appears to break the link between ∇(PV) = 0 and R < 1, suggesting Rayleigh-Kuo isn’t the dominant physics.

Ongoing work is concerned with exploring the relation between Rayleigh-Kuo and R with varying ∇. With these results, we want to quantify the effect of potential vorticity transport on zonal flow saturation and extend this to predator-prey models.