Abstract
The effects of an external mean flow on the modulational instability process of zonal flow in drift wave turbulence are theoretically studied based on Hasegawa–Mima (HM) turbulence model. Based on the coherent mode coupling approach, a dispersion relation of the zonal flow instability involving the external mean flow with a wave-type characterized by the amplitude |φ f |, radial wave number k f , and frequency ω f is derived. As an example, the zonal flow driven by ion temperature gradient (ITG) turbulence is sampled as the mean flow acting on the modulational process of zonal flow instability in electron temperature gradient (ETG) turbulence. It is shown that the growth rate of the zonal flow, γ q , is suppressed by the mean flow with a fitting relation γ q ≃γ q 0 -α|φ f | 2 k 2 f , where γ q 0 is the growth rate of the zonal flow 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. The suppression mechanism is investigated and found to originate from frequency mismatch due to an increase of the real frequency of zonal flow |Ω q |.
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