On the structure of the drifton phase space and its relation to the Rayleigh--Kuo criterion of the zonal-flow stability

TL;DR

This paper investigates the complex phase space of driftons in plasma models with zonal flows, revealing new behaviors such as accumulation and indefinite growth of momenta, and clarifies the limitations of geometrical optics in describing zonal flow stability.

Contribution

It introduces a detailed analysis of drifton phase space incorporating recent corrections, linking the Rayleigh--Kuo criterion to drifton trajectories and highlighting the failure of GO theory for intense zonal flows.

Findings

Driftons can accumulate and grow indefinitely, not just trapped or passing.

The Rayleigh--Kuo threshold corresponds to the dominance of runaway trajectories.

GO theory cannot describe the deterioration of intense zonal flows.

Abstract

The phase space of driftons (drift-wave quanta) is studied within the generalized Hasegawa--Mima collisionless-plasma model in the presence of zonal flows. This phase space is made intricate by the corrections to the drifton ray equations that were recently proposed by Parker [J. Plasma Phys. $\textbf{82}$, 95820602 (2016)] and Ruiz $\textit{et al.}$ [Phys. Plasmas $\textbf{23}$, 122304 (2016)]. Contrary to the traditional geometrical-optics (GO) model of the drifton dynamics, it is found that driftons can be not only trapped or passing, but they can also accumulate spatially while experiencing indefinite growth of their momenta. In particular, it is found that the Rayleigh--Kuo threshold known from geophysics corresponds to the regime when such "runaway" trajectories are the only ones possible. On one hand, this analysis helps visualize the development of the zonostrophic instability, particularly its nonlinear stage, which is studied here both analytically and through wave-kinetic simulations. On the other hand, the GO theory predicts that zonal flows above the Rayleigh--Kuo threshold can only grow; hence, the deterioration of intense zonal flows cannot be captured within a GO model. In particular, this means that the so-called tertiary instability of intense zonal flows cannot be adequately described within the quasilinear wave kinetic equation, contrary to some previous studies.