Drift wave turbulence and zonal flows

Abstract

Anomalously large radial transport levels in fusion devices is commonly believed to be the cause of small-scale edge localized electrostatic drift wave turbulence. We review the basic drift wave instability mechanism and show how poloidally elongated structures can self-consistently emerge from the small-scale turbulent motions through envelope modulation governed by the cubic nonlinear Schrödinger equation. There has been extensive study of the zonal flow - drift wave system recently, showing that zonal structures effectively reduce radial transport levels. We study the drift wave turbulence model due to Hasegawa and Wakatani (OHW), which upon subtle modification (MHW) also allows for zonal flow formation which is characteristic for the edge region of fusion devices. There is experimental evi- dence of long-range correlations; we investigate whether zonal flows give rise to such behavior in the hydrodynamic and quasi-adiabatic state of the OHW and MHW models. Rescaled range analysis gives no indication of long-range correlation. Struc- ture function analysis confirm this finding for the zonal flow free simulations where fluctuations are essentially Gaussian. Heavy tails in probability distributions of tur- bulent quantities due to the emergence of zonal flows in the quasi-adiabatic state of MHW complicate the analysis and increase in self-similarity parameters computed from structure functions cannot be used as proof for long-range correlation. The finding of this work is that significantly longer time-series are needed to clarify whether long-range correlations are an artefact of zonal structures or not.