Three-drift-wave interaction at finite parallel wavelength: Bifurcations and transition to turbulence

The generic properties of the nonlinear interaction of three drift waves with finite k∥ are investigated. The different types of stationary or quasistationary states are characterized by the bifurcation diagram in γ1, κ parameter space, where γ1 measures the mode excitation and κ the parallel wavenumber. The transition to turbulence corresponds exactly to the Ruelle–Takens picture: steady state→periodic solution→doubly periodic solution→turbulence, in contrast to the period-doubling route usually observed in low-dimensional dynamic systems. The transition to k∥=0, the model of Horton and Terry [Phys. Fluids 25, 491 (1982)], occurs at very small values of k∥.