Zonal-flow dynamics from a phase-space perspective

Abstract

The wave kinetic equation (WKE) describing drift-wave (DW) turbulence is widely used in studies of zonal flows (ZFs) emerging from DW turbulence. However, this formulation neglects the exchange of enstrophy between DWs and ZFs and also ignores effects beyond the geometrical-optics limit. We derive a modified theory that takes both of these effects into account, while still treating DW quanta ("driftons") as particles in phase space. The drifton dynamics is described by an equation of the Wigner-Moyal type, which is commonly known in the phase-space formulation of quantum mechanics. In the geometrical-optics limit, this formulation features additional terms missing in the traditional WKE that ensure exact conservation of the total enstrophy of the system, in addition to the total energy, which is the only conserved invariant in previous theories based on the WKE. Numerical simulations are presented to illustrate the importance of these additional terms. The proposed formulation can be considered as a phase-space representation of the second-order cumulant expansion, or CE2.

14 pages, 4 figures

References in corpus (3)

• Zonal flow generation in ion temperature gradient mode turbulence
• Zonal flow generation in collisionless trapped electron mode turbulence
• S3T stability of the homogeneous state of barotropic beta-plane turbulence

Cited by in corpus (4)

• Ponderomotive dynamics of waves in quasiperiodically modulated media
• Formation of solitary zonal structures via the modulational instability of drift waves
• Wave kinetic equation for inhomogeneous drift-wave turbulence beyond the quasilinear approximation
• Nonlinear saturation and oscillations of collisionless zonal flows