ALMOST 2-DIMENSIONAL TREATMENT OF DRIFT WAVE TURBULENCE

The approximation of two-dimensionality is studied and extended for electrostatic drift wave turbulence in a three-dimensional, magnetized plasma. It is argued on the basis of the direct interaction approximation that in the absence of parallel viscosity, purely 2-D solutions exist for which only modes with k∥ = 0 are excited, but that the 2-D spectrum is unstable to perturbations at nonzero k∥. A 1-D equation for the parallel profile gk⊥ (k∥) of the saturated spectrum at steady state is derived and solved, allowing for parallel viscosity; the spectrum has finite width in k∥, and hence finite parallel correlation length, as a result of nonlinear coupling. The enhanced energy dissipation rate, a 3-D effect, may be incorporated in the 2-D approximation by a suitable renormalization of the linear dissipation term. An algorithm is presented that reduces the 3-D problem to coupled 1- and 2-D problems. Numerical results from a 2-D spectral direct simulation, thus modified, are compared with the results from the corresponding 3-D (unmodified) simulation for a specific model of drift wave excitation. Damping at high k∥ is included. It is verified that the 1-D solution for gk⊥ (k∥) accurately describes the shape and width of the 3-D spectrum, and that the modified 2-D simulation gives a good estimate of the 3-D energy saturation level and distribution E(k⊥). © 1990 American Institute of Physics.