Investigating Dimits Shift and Zonal Flows in Toroidal Ion Temperature Gradient Driven Turbulence Using Weak Turbulence Closure Models*

In toroidal ion temperature gradient (ITG) driven turbulence, there exists a range of driving gradients for which heat flux is suppressed relative to the growth of linear instability. Known as the Dimits regime, an unexplained feature of this particular parameter space is the observation of temporally intermittent turbulent fluctuations and resulting transport. Previous research connected this suppression to resonant energy transfer among triads of interacting modes, but did not account for intermittency in the fluctuations. The primary goal of this project is to investigate these appreciably non-Gaussian statistical features and their relation to the Dimits Shift. The main result is derivation and solution of a differential equation for zonal flow Fourier-autocorrelation (ZFFA) via application of weak turbulence closure to a two field fluid model for toroidal ITG. These types of functions characterize the manner in which the zonal flow of a given wavenumber will decorrelate from itself due to the presence of nonlinear interactions. Using numerical simulations, analytically expected exponential decay of the ZFFA is confirmed.