Controlling turbulence in the complex Ginzburg-Landau equation

Controlling turbulence in the complex Ginzburg-Landau equation (CGLE) is investigated. The CGLE is generalized to include gradient force. Local injections (pinnings) are applied for turbulence control. It is found that local injections are effective in eliminating turbulence. In particular, for large gradient force, it is possible to suppress fully developed turbulence by adding a few injections much less in number than the number of positive Lyapunov exponents of the system. The high efficiency of controlling is heuristically explained, based on the spatial correlation length and space-time-variable transformation.