Investigation of drift-wave instability in the presence of zonal flows using spatial averaging

The interaction of micro-scale turbulence with zonal flows is one of the key topics in magnetically confined plasma research. We study the stability of drift waves in the presence of large scale flows in the Hasegawa-Wakatani system using spatial averaging. The dispersion relation obtained by this treatment is independent of the radial coordinate and includes resonant terms, which become dominant when the phase speed of the drift wave is comparable to the local advection speed of zonal flow. This dispersion relation is then solved numerically to yield linear growth rates for a small drift wave perturbation against a zonal flow background. The growth rates are similar to those found without zonal flows, when far from the resonant conditions. Close to resonance, both the real frequency and the growth rates differ significantly from the usual case. The stability of zonal flows is also examined.