Phase Dynamics and Energetics in Drift Wave-Zonal Flow Turbulence*

The roles of wave phase structure and evolution in zonal flow dynamics are investigated. Previous work (Guo, Diamond; 2016) has noted that wave phase curvature is sufficient to produce a gradient in the Reynolds force and thus to drive zonal flow formation — even for turbulence of homogeneous fluctuation intensity. In this study, we investigate the energetics and nonlinear evolution of the process. For energetics, refraction (i.e. changes in phase gradient due to Z.F. shear) allows wave energy — and thus the ZF — to evolve at fixed wave amplitude. Using the phase evolution equation derived for the Hasegawa-Mima model, we prove energy conservation between waves and ZF, for fixed wave potential intensity. By separating the mesoscale phase into mean and fluctuation, we show that phase evolution induces ZF formation due to phase gradient shocks. Then, we investigate how linear and nonlinear feedback of the gradient affect the synchronization of the shock structure. Finally, we consider dynamic amplitude to explore the full predator-prey relationship between ZF (predator) and drift waves (prey).