Spectral properties and statistics of resistive drift-wave turbulence

Resistive drift-wave turbulence is studied by high-resolution numerical simulation in the limit of small viscosity (high Reynolds numbers), such that the adiabaticity parameter V is the only relevant parameter. Energy spectra exhibit a maximum at some wave-number kc, and a power law behavior for k> k+ Statistics in this range are non-Gaussian indicating strong intermittency, but are perfectly Gaussian for kg k+,. Drift-wave turbulence is generally believed to cause anomalous transport in magnetically confined plasmas such as those in tokamaks and stellarators. Density and potential fluctuations are particularly strong in the cool plasma edge region, where collisional effects are most important to drift-waves. A simple twodimensional model to describe drift-wave turbulence in this regime is due to Hasegawa and Wakatani [ 1,2]. It consists of two equations for the potential and density fluctuations v, (x, v) , n (x, y ) in a plasma with a constant mean density gradient dnJdx in the x direction and a magnetic field essentially in the z direction, a,w+miksf(p-n)+9y a,n+~vn+a,~=u(~-n)+~n, v=ixva,, co= v=p ) (1) (2) written in the usual dimensionless form: x, y+ x/~s, Y/P,, t+ (tfh) (A/J%), F+ (edT&,lP,, II-+ (n/no) (L/P,), L=~o/ IdnolW; A and Qi are the ion Larmor radius and frequency, respectively. V is called the adiabaticity parameter due to the electron parallel friction, i.e. resistivity q, %= ( Te/noq)k~, and 9”, 9” are the viscous and diffusive dissipation terms to be specified below. Apart from its potential application to anomalous plasma transport, the Hasegawa-Wakatani model is also interesting in its own right as an autonomous (i.e. self-exciting) system of 2-D turbulence. For VK 1 Eq. ( 1) decouples to the 2-D Navier-Stokes equation, while n is essentially a passive scalar. In the opposite limit V>> 1, the electrons are almost adiabatic n-v, C+Z n, and Eqs. ( 1) and (2) are essentially equivalent to the Hasegawa-Mima equation [ 3 1. For the HasegawaWakatani model, the energy E = $$ d2x ( v2 + n ‘) and the generalized enstrophy IV= f J d2x (n-w) ‘, which are the invariants of the Hasegawa-Mima equation, follow the equations