Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation

Abstract

Inhomogeneous drift-wave turbulence can be modeled as an effective plasma where drift waves act as quantumlike particles and the zonal-flow velocity serves as a collective field through which they interact. This effective plasma can be described by a Wigner-Moyal equation (WME), which generalizes the quasilinear wave-kinetic equation (WKE) to the full-wave regime, i.e., resolves the wavelength scale. Unlike waves governed by manifestly quantumlike equations, whose WMEs can be borrowed from quantum mechanics and are commonly known, drift waves have Hamiltonians very different from those of conventional quantum particles. This causes unusual phase-space dynamics that is typically not captured by the WKE. We demonstrate how to correctly model this dynamics with the WME instead. Specifically, we report full-wave phase-space simulations of the zonal-flow formation (zonostrophic instability), deterioration (tertiary instability), and the so-called predator-prey oscillations. We also show how the WME facilitates analysis of these phenomena, namely, (i) we show that full-wave effects critically affect the zonostrophic instability, particularly, its nonlinear stage and saturation; (ii) we derive the tertiary-instability growth rate; and (iii) we demonstrate that, with full-wave effects retained, the predator-prey oscillations do not require zonal-flow collisional damping, contrary to previous studies. We also show how the famous Rayleigh-Kuo criterion, which has been missing in wave-kinetic theories of drift-wave turbulence, emerges from the WME.

References in corpus (7)

• Bifurcation in electrostatic resistive drift wave turbulence
• Gyrokinetic continuum simulation of turbulence in a straight open-field-line plasma
• Zonal-flow dynamics from a phase-space perspective
• On Nonlocal Energy Transfer via Zonal Flow in the Dimits Shift
• Statistical state dynamics of jet/wave coexistence in barotropic beta-plane turbulence
• White-light parametric instabilities in plasmas
• Dynamics of Zonal Flows: Failure of Wave-Kinetic Theory, and New Geometrical Optics Approximations

Cited by in corpus (12)

• Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
• On the Rayleigh--Kuo criterion for the tertiary instability of zonal flows
• Wave-kinetic approach to zonal-flow dynamics: recent advances
• On the structure of the drifton phase space and its relation to the Rayleigh--Kuo criterion of the zonal-flow stability
• Formation of solitary zonal structures via the modulational instability of drift waves
• Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation
• Bandwidth effects in stimulated Brillouin scattering driven by partially incoherent light
• Theory of the tertiary instability and the Dimits shift within a scalar model
• Nonlinear saturation and oscillations of collisionless zonal flows
• Structure formation in turbulence as instability of effective quantum plasma
• Solitary zonal structures in subcritical drift waves: a minimum model
• Collisional whistler instability and electron temperature staircase in inhomogeneous plasma