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

TL;DR

This paper critically examines the limitations of existing wave kinetic theories in describing the dynamics of zonal flows and introduces new geometrical optics approximations that incorporate higher-order derivatives of the mean flow.

Contribution

It identifies the failure of traditional wave kinetic equations for large-scale flows and proposes novel geometrical optics approximations including second and third derivatives of the mean flow.

Findings

Traditional wave kinetic equations are pathological for large-scale flows.

New geometrical optics approximations incorporate higher derivatives of the mean flow.

One approximation leads to a new wave kinetic equation valid for quasi-static flows.

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.