Space-time statistics of drift wave turbulence

Recent probe studies in TEXT-U using conditional probability statistics have shown (1) Gaussian-like statistics [kurtosis 3.1, skewness 0.1] and (2) correlation decay rates in time and space with a finite dependence on the amplitude of the floating potential condition. Motivated by these experiments, the authors have modeled the turbulence as a gas of interactive vortices and waves. They compute correlation functions when conditioned by the requirement that the amplitude of the reference signal exceed a level appropriate for vortex trapping. The work extends the earlier study of the statistics of drift wave turbulence. The important conclusion emerging from the experimental data, and shown here to follow from the computer simulations is that turbulent fields with Gaussian-like space-time statistics as measured by the kurtosis and skewness can be composed of a gas of interacting vortices satisfying the trapping condition. The condition for Gaussian-like statistics is that the vortex gas not be too dilute. A general formula for the relative contributions of the waves and the vortices (or coherent structures in the presence of magnetic shear) is given. In the absence of waves the condition reduces to the requirement that the packing fraction fp = nvπ left-angle R2 right-angle > 1/3 where nv = Nv/LxLy is the number of vortices of radius R per unit area. The Gaussian-like statistics in the wave dominated case, are given in a reference for the dissipative (Terry-Horton) driftwave equation. The statistics for other drift wave models have now also been studied. As an example, for the Hasegawa-Mima equation a 5 x 5 lattice of dipole vortices with R = 6ρs, packed at t = 0 to give a kurtosis of 2.8 and zero skewness, evolve by ∼100 Ln/cs to a state of coalescing vortices with kurtosis 3.0 ± 0.1 and skewness 0.1 to 0.2