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...

The regulation of turbulent transport by zonal flows is studied experimentally on a flux surface of the stellarator experiment TJ-K. Data of 128 Langmuir probes at different toroidal and poloidal positions on a single flux surface enable us to measure simultaneously the zonal flow activity and the turbulent transport in great detail. A reduction of turbulent transport by 30% during the zonal fl...

Plasma shaping e¤ects, such as elongation, triangularity and Shafranov shift have long been considered an important ingredient in improving tokamak performance. It is known that the growth rate of ion temperature gradient (ITG) turbulence can be regulated by these shaping e¤ects and that the ITG turbulence level can also be regulated by zonal ‡ow. Moreover, recent numerical simulation shows tha...

This paper surveys the basic ideas and results on fundamental models of drift wave turbulence, the formation of zonal flows, shear suppression of turbulence and transport, coupled drift wave and zonal flow dynamics, and application to transport bifurcations and transitions. Application to vortex dynamics and zonal flow phenomena in EMHD systems are discussed, as well. These are relevant to aspe...

The main purpose of cementing of the well is to provide effective zonal isolation for the entire life of wells. The standard cements cannot prevent loss of zonal isolation when the stress level in the well cement is severely fluctuated. Since elastic cements improve elastic properties, recently, a number of studies have been done in this area. For this purpose, a nanoparticle, named EX-RIPI, wa...

Zonal ‡ow helps reduce and control the level of ion temperature gradient (ITG) turbulence in a tokamak. The collisional damping of zonal ‡ow has been estimated by Hinton and Rosenbluth (H-R). Their calculation shows that the damping of zonal ‡ow is closely related to the frequency response of neoclassical polarization of the plasma. Based on a variational principle, H-R calculated the neoclassi...

We propose a quantitative model of ion temperature gradient driven turbulence in toroidal magnetized plasmas. In this model, the turbulence is regulated by zonal flows, i.e. mode saturation occurs by a zonal-flow-mediated energy cascade (‘shearing’), and zonal flow amplitude is controlled by nonlinear decay. Our model is tested in detail against numerical simulations to confirm that both its as...

Gyrokinetic δf particle simulation is used to investigate the nonlinear saturation mechanisms in collisionless trapped electron mode (CTEM) turbulence. It is found that the importance of zonal flow is parameter sensitive and is well characterized by the shearing rate formula. The effect of zonal flow is empirically found to be sensitive to temperature ratio, magnetic shear and electron temperat...

Neoclassical shielding is the dominant mechanism reducing the collisionless zonal flow in a tokamak. Previously, this phenomenon was analyzed in the case of an essentially homogeneous equilibrium since the wavelength of the zonal flow perturbation was assumed to be much less than the scale length of background plasma parameters. This assumption is not appropriate in a tokamak pedestal. Therefor...

The pair of groups, symmetric group S2n and hyperoctohedral group Hn , form a Gelfand pair. The characteristic map is a mapping from the graded algebra generated by the zonal spherical functions of (S2n, Hn) into the ring of symmetric functions. The images of the zonal spherical functions under this map are called the zonal polynomials. A wreath product generalization of the Gelfand pair (S2n, ...