Zonal-flow dynamics from a phase-space perspective

TL;DR

This paper introduces a modified wave kinetic equation for drift-wave turbulence that conserves enstrophy and energy more accurately by incorporating effects beyond the geometrical-optics limit, using a phase-space approach.

Contribution

It derives a new phase-space formulation of drift-wave turbulence that accounts for enstrophy exchange and effects beyond geometrical optics, improving conservation properties.

Findings

The new formulation conserves total enstrophy and energy.

Numerical simulations demonstrate the significance of additional terms.

The approach links to a phase-space representation of CE2.

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.