Dynamics of Zonal Flows: Failure of Wave-Kinetic Theory, and New Geometrical Optics Approximations

Abstract

The self-organization of turbulence into regular zonal flows can be fruitfully investigated with quasilinear methods and statistical descriptions. A wave kinetic equation that assumes asymptotically large-scale zonal flows is pathological. From an exact description of quasilinear dynamics emerges two better geometrical optics approximations. These involve not only the mean flow shear but also the second and third derivative of the mean flow. One approximation takes the form of a new wave kinetic equation, but is only valid when the zonal flow is quasi-static and wave action is conserved.

12 pages, 3 figures. See version 1 for conventional geophysical notation and version 2 for conventional plasma notation

References in corpus (9)

• Bifurcation in electrostatic resistive drift wave turbulence
• Direct Statistical Simulation of Out-of-Equilibrium Jets
• The Generalized Quasilinear Approximation: Application to Zonal Jets
• Astrophysical Fluid Dynamics via Direct Statistical Simulation
• Zonal flow generation in ion temperature gradient mode turbulence
• Statistical simulation of the magnetorotational dynamo
• Statistical state dynamics of jet/wave coexistence in barotropic beta-plane 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 (17)

• Zonally dominated dynamics and Dimits threshold in curvature-driven ITG turbulence
• Zonal-flow dynamics from a phase-space perspective
• On Nonlocal Energy Transfer via Zonal Flow in the Dimits Shift
• On the Rayleigh--Kuo criterion for the tertiary instability of zonal flows
• A Flux-Balanced Fluid Model for Collisional Plasma Edge Turbulence: Model Derivation and Basic Physical Features
• Wave kinetics of drift-wave turbulence and zonal flows beyond the ray approximation
• 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
• Nonlinear saturation and oscillations of collisionless zonal flows
• Structure formation in turbulence as instability of effective quantum plasma
• Magnetic eddy viscosity of mean shear flows in two-dimensional magnetohydrodynamics
• Solitary zonal structures in subcritical drift waves: a minimum model
• Numerical simulation of the geometrical-optics reduction of CE2 and comparisons to quasilinear dynamics
• Density operator approach to turbulent flows in plasma and atmospheric fluids
• Statistical theory of the broadband two-plasmon decay instability