A comprehensive review of zonal flow phenomena in plasmas is presented. While the emphasis is on zonal flows in laboratory plasmas, planetary zonal flows are discussed as well. The review presents the status of theory, numerical simulation and experiments relevant to zonal flows. The emphasis is on developing an integrated understanding of the dynamics of drift wave-zonal flow turbulence by combining detailed studies of the generation of zonal flows by drift waves, the back-interaction of zonal flows on the drift waves, and the various feedback loops by which the system regulates and organizes itself. The implications of zonal flow phenomena for confinement in, and the phenomena of fusion devices are discussed. Special attention is given to the comparison of experiment with theory and to identifying directions for progress in future research. © 2005 IOP Publishing Ltd.

A calculation which describes the spin-up of toroidal plasmas by the radial propagation of turbulence fronts with broken parallel symmetry is presented. The associated flux of parallel momentum is calculated by using a two-scale direct-interaction approximation in the weak turbulence limit. We show that fluctuation momentum spreads faster than mean flow momentum. Specifically, the turbulent flux of wave momentum is stronger than the momentum pinch. The scattering of fluctuation momentum can induce edge-core coupling of toroidal flows, as observed in experiments.

A theory to describe the conversion of poloidal momentum into toroidal momentum by phase space structures in trapped ion resonance driven turbulence is presented. In trapped ion resonance driven turbulence, phase space structures are expected to form and can contribute to transport by exerting dynamical friction. Toroidal momentum flux by dynamical friction is calculated. It is shown that dynamical friction exerted on trapped ion granulations can mediate momentum transfer between poloidal and toroidal flows. The conversion coefficient is calculated as measurable, which can be validated in current devices. © 2013 IOP Publishing Ltd.

The role of zonal flows (ZFs) in the formation of an internal transport barrier in a toroidal helical plasma is analyzed. The turbulent transport coefficient is shown to be suppressed when the plasma state changes from the branch of a weak negative radial electric field to the strong positive one. This new transition of turbulent transport is caused by the change of the damping rate of the ZFs. It is clearly demonstrated, theoretically and experimentally, that the damping rate of the ZFs governs the global confinement of toroidal plasmas. © 2007 American Institute of Physics.

The influence of the turbulence spreading is studied on the self-sustained turbulence which is induced by the subcritical instability. It is found that there is a minimum system size that can sustain the self-sustained turbulence, and an analytic formula is derived. The generalization of the Maxwell's construction rule is also derived. ©2005 The Physical Society of Japan.

The bicoherence of fluctuations in a system of drift waves and zonal flows is discussed. In strong drift-wave turbulence, where broadband fluctuations are excited, the bicoherence is examined. A Langevin equation formalism of turbulent interactions allows us to relate the bicoherence coefficient to the projection of nonlinear force onto the test mode. The dependence of the summed bicoherence on the amplitude of zonal flows is clarified. The importance of observing biphase is also stressed. The results provide a basis for measurement of nonlinear interaction in a system of drift waves and zonal flow. © 2005 American Institute of Physics.

© 2014 AIP Publishing LLC. A theory to describe basic characterization of ion temperature gradient driven turbulence with strong trapped ion resonance is presented. The role of trapped ion granulations, clusters of trapped ions correlated by precession resonance, is the focus. Microscopically, the presence of trapped ion granulations leads to a sharp (logarithmic) divergence of two point phase space density correlation at small scales. Macroscopically, trapped ion granulations excite potential fluctuations that do not satisfy dispersion relation and so broaden frequency spectrum. The line width from emission due only to trapped ion granulations is calculated. The result shows that the line width depends on ion free energy and electron dissipation, which implies that non-adiabatic electrons are essential to recover non-trivial dynamics of trapped ion granulations. Relevant testable predictions are summarized.

Excitation of the turbulence in the range of drift wave frequency and zonal flow in magnetized plasmas is analyzed. Nonlinear stabilization effect on zonal flow drive is introduced, and the steady state solution is obtained. The condition for the onset of turbulent transport is obtained and partition ratio of fluctuation energy into turbulence and zonal flows is derived. The turbulent transport coefficient, which includes the effect of zonal flow, is also obtained. Analytic result and direct numerical simulation show a good agreement. © 2005 American Institute of Physics.

Zonal flows, which means azimuthally symmetric band-like shear flows, are ubiquitous phenomena in nature and the laboratory. It is now widely recognized that zonal flows are a key constituent in virtually all cases and regimes of drift wave turbulence, indeed, so much so that this classic problem is now frequently referred to as "drift wave-zonal flow turbulence." In this review, new viewpoints and unifying concepts are presented, which facilitate understanding of zonal flow physics, via theory, computation and their confrontation with the results of laboratory experiment. Special emphasis is placed on identifying avenues for further progress. © 2006 American Institute of Physics.