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

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. $\text{82}$, 95820602 (2016)] and Ruiz $\text{et al.}$ [Phys. Plasmas $\text{23}$, 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.

arXiv commentAssociated dataset available at http://dx.doi.org/10.5281/zenodo.1244318

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Cited by in corpus (14)

• Theory of the tertiary instability and the Dimits shift from reduced drift-wave models
• Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence
• 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
• Theory of the tertiary instability and the Dimits shift within a scalar model
• Nonlinear saturation and oscillations of collisionless zonal flows
• Solitary zonal structures in subcritical drift waves: a minimum model
• Nearly integrable flows and chaotic tangles in the Dimits shift regime of plasma edge turbulence
• Hamiltonian Structure and Nonlinear Stability of Steady Solutions of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields
• Guiding Center Derivation of the Generalized Hasegawa-Mima Equation for Drift Wave Turbulence in Curved Magnetic Fields
• Detecting Shearless Phase-Space Transport Barriers in Global Gyrokinetic Turbulence Simulations with Test Particle Map Models