On the stability of drift wave spectra with respect to zonal flow excitation

Abstract

A simple criterion that allows one to determine whether or not a given wave spectrum will generate zonal flows, is derived and analyzed. In the context of a coupled drift wave–zonal turbulence, the results are pertinent to the limit of small zonal flow damping, γd→0, in which previous analyses found that the turbulence vanishes. However, the practically important issue of the drift wave amplitude threshold for zonal flow excitation was not resolved. In its formal mathematical appearance, the criterion obtained is similar to the well-known Penrose criterion that is used for stability analysis of stellar distributions and particle distributions in plasmas. By contrast, the derived criterion, being applied to wave quanta rather than to particle distribution, shows that even “normal” (wave density decaying with wave number) distributions with an intensity above the threshold should generate zonal flows. This clearly points at the ubiquity of the latter.