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 ω_q = Ω_q + iγ_q is derived, which depends on the external mean flow's amplitude |φ_f| and radial wave number k_f. 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 γ_q is found to be suppressed, showing a relation γ_q = γ_q0(1-α|φ_f|²k_f² ), where γ_q0 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|φ_f²|k_f² ≈ 1. Meanwhile, the suppression is accompanied by an increase of the real frequency |Ω_q|. The underlying physical mechanism of the suppression is discussed.