In Search of the Elusive Zonal Flow Using Cross-Bicoherence Analysis

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.