Three-dimensional computations of turbulence arising from the nonlinear collisional drift wave equations are carried out. The flux-surface-based coordinate system is aligned with the magnetic field, and the geometry is that of an actual model tokamak with arbitrary poloidal cross section. The physical periodicity constraint is rigorously respected. The results show that the dominant process arising from this system is the three-dimensional version of the collisional drift wave nonlinear instability, in which fluctuation free energy transfer among parallel wavelengths plays an enhanced role. Poloidal asymmetry in the fluctuations and associated transport are found to result primarily from the poloidal variation in the ion polarization drift and not the more traditional ballooning (magnetic curvature) effects. Magnetic curvature is found to be very important only in the case of reversed magnetic shear: with it, reversing the shear causes a drop in the thermal energy flux by a factor of three. The contrast with concurrent work on ballooning is suggested to result from the latter's neglect of the electron temperature dynamics. As in previous results of two-dimensional slab computations, the electron temperature gradient is the principal free energy source. The turbulence appears to be non-local over the radial range of the 4 cm covered by the computations; the non-locality is a form of weighted averaging of the free energy sources and sinks by the turbulence, and is sufficient to explain the rise in relative amplitude with increasing radius since the absolute amplitude is relatively constant. Initial tests with an isothermal ion pressure suggest that the ion dynamics could make up the quantitative difference between these results and the experimental observations, once the ion temperature is properly incorporated.
Pinch effect in two-dimensional turbulence