Effect of Mean Flow on the Interaction between Turbulence and Zonal Flow

Abstract

The effects of an external mean flow on the generation of zonal flow in drift wave turbulence are theoretically studied in terms of a modulational instability analysis. A dispersion relation for the zonal flow instability having complex frequency ωq = Ωq + iγq is derived, which depends on the external mean flow's amplitude |φf| and radial wave number kf. As an example, we chose an ion temperature gradient (ITG) turbulence-driven zonal flow as the mean flow acting on an electron temperature gradient (ETG) turbulence-zonal flow system. The growth rate of the zonal flow γq is found to be suppressed, showing a relation γq = γq0(1-α|φf|2kf2 ), where γq0 is the growth rate in the absence of mean flow and α is a positive numerical constant. This formula is applicable to a strong shearing regime where the zonal flow instability is stabilized at α|φf2|kf2 ≈ 1. Meanwhile, the suppression is accompanied by an increase of the real frequency |Ωq|. The underlying physical mechanism of the suppression is discussed.