A recently introduced tool for the analysis of turbulence, wavelet bicoherence [van Milligen, Hidalgo, and Sánchez, Phys. Rev. Lett. 16, 395 (1995)], is investigated. It is capable of detecting phase coupling—nonlinear interactions of the lowest (quadratic) order—with time resolution. To demonstrate its potential, it is applied to numerical models of chaos and turbulence and to real measurements. It detected the coupling interaction between two coupled van der Pol oscillators. When applied to a model of drift wave turbulence relevant to plasma physics, it detected a highly localized coherent structure. Analyzing reflectometry measurements made in fusion plasmas, it detected temporal intermittency and a strong increase in nonlinear phase coupling coinciding with the L/H (low-to-high confinement mode) transition.

We investigate the dynamics of the low(L) $\to$ high(H) transition using a time-dependent, one dimensional (in radius) model which self-consistently describes the time evolution of zonal flows (ZFs), mean flows (MFs), poloidal spin-up, and density and pressure profiles. The model represents the physics of ZF and MF competition, turbulence suppression via $E\times B$ shearing, and poloidal flows driven by turbulence. Numerical solutions of this model show that the $\mathrm{L}\to \mathrm{H}$ transition can occur via an intermediate phase (I-phase) which involves oscillations of profiles due to ZF and MF competition. The I-phase appears as a nonlinear transition wave originating at the edge boundary and propagates inward. Locally, I-phase exhibits the characteristics of a limit-cycle oscillation. All these observations are consistent with recent experimental results. We examine the trigger of the $\mathrm{L}\to \mathrm{H}$ transition, by defining a ratio of the rate of energy transfer from the turbulence to the zonal flow to the rate of energy input into the turbulence. When the ratio exceeds order unity, ZF shear gains energy, and a net decay of the turbulence is possible, thus triggering the $\mathrm{L}\to \mathrm{H}$ transition. Numerical calculations indicate that the $\mathrm{L}\to \mathrm{H}$ transition is triggered by this peak of the normalized ZF shearing. Zonal flows act as “reservoir,” in which to store increasing fluctuation energy without increasing transport, thus allowing the mean flow shear to increase and lock in the transition. A counterpart of the L $\to$ $\mathrm{I}\to \mathrm{H}$ transition, i.e., an $\mathrm{L}\to \mathrm{H}$ transition without I-phase, is obtained in a fast power ramp, for which I-phase is compressed into a single burst of ZF, which triggers the transition. Effects of neutral charge exchange on the $\mathrm{L}\to \mathrm{H}$ transition are studied by varying ZF damping and neoclassical viscosity. Results show that the predicted $\mathrm{L}\to \mathrm{H}$ transition power increases when either ZF damping or viscosity increase, suggesting a link between recycling, ZF damping, and the $\mathrm{L}\to \mathrm{H}$ threshold. Studies of fueling effects on the transition and pedestal structure with an emphasis on the particle pinch are reported.

We show that the modulational instability growth rate of zonal flows is determined directly from the quasilinear wave kinetic equation. We also demonstrate the relation between zonal-flow growth and the cross bispectrum of the high-frequency drift-wave-driven Reynolds stress and the low-frequency plasma potential by explicit calculation. Experimental measurements of the spatiotemporal evolution of the spectrum integrated bicoherence at the $L\to H$ transition near the edge shear layer indicate a modification in the nonlinear phase coupling, which might be linked to the generation of sheared $\mathbf{E}\times \mathbf{B}$ flows.

The spatiotemporal behavior of the interaction between turbulence and flows has been studied close to the L-H transition threshold conditions in the edge region ($\rho \ge 0.7$) of TJ-II plasmas. The temporal dynamics of the interaction displays an oscillatory behavior with a characteristic predator-prey relationship. The spatial evolution of this turbulence-flow oscillation pattern has been measured, showing both radial outward and inward propagation velocities of the turbulence-flow front. The results indicate that the edge shear flow linked to the L-H transition can behave either as a slowing-down, damping mechanism of outward propagating turbulent-flow oscillating structures, or as a source of inward propagating turbulence-flow events.