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The self-organization of turbulence into regular zonal flows can befruitfully investigated with quasilinear methods and statistical descriptions.A wave kinetic equation that assumes asymptotically large-scale zonal flows ispathological. From an exact description of quasilinear dynamics emerges twobetter geometrical optics approximations. These involve not only the mean flowshear but also the second and third derivative of the mean flow. Oneapproximation takes the form of a new wave kinetic equation, but is only validwhen the zonal flow is quasi-static and wave action is conserved.

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