Zonal-Flow Dynamics and Size Scaling of Anomalous Transport

Nonlinear equations for the slow space-time evolution of the radial drift-wave envelope and zonal flow amplitude have been self-consistently derived for a model nonuniform tokamak equilibrium within the coherent four-wave drift wave-zonal flow modulation interaction model of Chen, Lin, and White [Phys. Plasmas 7, 3129 (2000)]. Solutions clearly demonstrate turbulence spreading due to nonlinearly enhanced dispersiveness and, consequently, the device-size dependence of the saturated wave intensities and transport coefficients.

Figure 1

Radial structure of the real part of the wave fields, $\mathrm{R}\mathrm{e}P$ (black), $\mathrm{R}\mathrm{e}S$ (red), and $\mathrm{R}\mathrm{e}Z$ (green), at three subsequent times $\tau =20$ (left), $\tau =50$ (center), and $\tau =125$ (right), for $A=1.15$ and $L=200$. The radial domain where the pump is linearly stable is also indicated.

Figure 2

Characteristic squared width of the wave fields normalized to $L^2$ as a function of time, for $A=1.2$ and $L=200$. Color code is the same as in Fig. 1.

Figure 3

Drift wave intensity $⟨\overline{I}⟩$ vs $L$ after spatial averaging on one-fifth of the linearly unstable domain. The three curves refer to $A=1.15$, $A=1.2$, and $A=1.3$.