Zonal flow dynamics: phase-space simulations beyond the ray approximation

Traditional phase-space (wave-kinetic) modeling of drift-wave turbulence and zonal flows invokes the geometrical-optics (ray) approximation, i.e., treating the drift waves as point particles interacting with the zonal flow fields. Recently, a Wigner-Moyal model of this system has been developed, which retains full-wave effects by treating the drift waves as quantum-like particles (Ruiz et al. 2016, PoP 23, 122304). We present numerical simulations, based on the Wigner-Moyal model, of zonal flow formation (zonostrophic instability), deterioration (tertiary instability), and oscillation (of predator-prey type) (Zhu et al. 2018, PRE 97, 053210). Certain types of stationary and propagating nonlinear coherent structures are also investigated. We demonstrate the importance of full-wave effects by comparing these results with wave-kinetic simulations.