领域：学术论文 · 自然科学

Zonal ﬂows, by which we mean azimuthally symmetric band-like shear ﬂows, are a ubiquitous phenomena in nature and the laboratory. The well-known examples of the Jovian belts and zones, and the terrestrial atmospheric jet stream are familiar to nearly everyone—the latter especially to travellers enduring long, bumpy airplane rides against strong head winds. Zonal ﬂows are also present in the Venusian atmosphere (which rotates faster than the planet does!) and occur in the solar tachocline, where they play a role in the solar dynamo mechanism. In the laboratory, the importance of sheared E × B ﬂows to the development of L-mode conﬁnement, the L-to-H transition and internal transport barriers(ITBs) is now well and widely appreciated.

While many mechanisms can act to trigger and stimulate the growth of sheared electric ﬁelds (i.e. proﬁle evolution and transport bifurcation, neoclassical effects, external momentum injection, etc) certainly one possibility is via the self-generation and ampliﬁcation of E × B ﬂows by turbulent stresses (i.e. the turbulent transport of momentum). Of course, this is the same mechanism as that responsible for zonal ﬂow generation. It should be emphasized that it is now widely recognized and accepted that zonal ﬂows are a key constituent in nearly 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’. This paradigm shift occurred on account of the realization that zonal ﬂows are ubiquitous in dynamical models used for describing fusion plasmas (i.e. ITG, TEM, ETG, resistive ballooning and interchange, etc) in all geometries and regimes (i.e. core, edge, etc), and because of the realization that zonal ﬂows are a critical agent of self-regulation for drift wave transport and turbulence. Both theoretical work and numerical simulation made important contributions to this paradigm shift. Indeed, for the case of low collisionality plasmas, a signiﬁcant portion of the available free energy is ultimately deposited in the zonal ﬂows. Figure 1 presents energy ﬂow charts which illustrate the classic paradigm of drift wave turbulence and the new paradigm of drift wave–zonal ﬂow turbulence. The study of zonal ﬂow has had a profound impact on fusion research. For instance, the proper treatment of the zonal ﬂow physics has resolved some of the confusion concerning the prospect of burning plasma, as has been discussed by Rosenbluth and collaborators in conjunction with the design of the International Thermonuclear Experimental Reactor (ITER). At the same time, the understanding of the turbulence–zonal ﬂow system has advanced the understanding of self-organization processes in nature.

We note here that, while zonal ﬂows have a strong inﬂuence on the formation of transport barriers, the dynamics of barriers and transitions involve evolutions of both the mean E × B ﬂow as well as the zonal E × B ﬂow. The topics of mean Er dynamics, transport barriers and conﬁnement regime transitions are beyond the scope of this review.

In the context of tokamak plasmas, zonal ﬂows are n = 0 electrostatic potential ﬂuctuations with ﬁnite radial wavenumber. Zonal ﬂows are elongated, asymmetric vortex modes, and thus have zero frequency. They are predominantly poloidally symmetric as well, though some coupling to low-m sideband modes may occur. On account of their symmetry, zonal ﬂows cannot access expansion free energy stored in temperature, density gradients, etc, and are not subject to Landau damping. These zonal ﬂows are driven exclusively by nonlinear interactions, which transfer energy from the ﬁnite-n drift waves to the n = 0 ﬂow. Usually, such nonlinear interactions are three-wave triad couplings between two high k drift waves and one low q zonal ﬂow excitation. In position space, this energy transfer process is simple one whereby Reynolds work is performed on the ﬂow by the wave stresses. Two important consequences of this process of generation follow directly. First, since zonal ﬂow production is exclusively via nonlinear transfer from drift waves, zonal ﬂows must eventually decay and vanish if the underlying drift wave drive is extinguished. Thus, zonal ﬂows differ in an important way from mean E × B ﬂows, which can be sustained in the absence of turbulence (and are, in strong H-mode and ITB regimes). Second, since zonal ﬂows are generated by nonlinear energy transfer from drift waves, their generation naturally acts to reduce the intensity and level of transport caused by the primary drift wave turbulence. Thus, zonal ﬂows necessarily act to regulate and partially suppress drift wave turbulence and transport. This is clear from numerical simulations, which universally show that turbulence and transport levels are reduced when the zonal ﬂow generation is (properly) allowed. Since zonal ﬂows cannot 
tap expansion free energy, are generated by nonlinear coupling from drift waves, and damp primarily (but not exclusively) by collisional processes, they constitute a signiﬁcant and benign (from a conﬁnement viewpoint) reservoir or repository for the available free energy of the system.

Another route to understanding the effects of zonal ﬂow on drift waves is via the shearing paradigm. From this standpoint, zonal ﬂows produce a spatio-temporally complex shearing pattern, which naturally tends to distort drift wave eddies by stretching them, and in the process generates large kr. Of course, at smaller scales, coupling to dissipation becomes stronger, resulting in a net stabilizing trend. The treatment of zonal ﬂow shearing differs from that for mean ﬂow shearing on account of the complexity of the ﬂow pattern. Progress here has been facilitated by the realization that a statistical analysis is possible. This follows from the fact that the autocorrelation time of a drift wave-packet propagating in a zonal ﬂow ﬁeld is usually quite short, and because the drift wave rays are chaotic. Hence, signiﬁcant advances have been made on calculating the ‘back reaction’ of zonal ﬂows on the underlying drift wave ﬁeld within the framework of random shearing, using wave kinetics and quasilinear theory. Conservation of energy between drift waves and zonal ﬂows has been proved for the theory, at the level of a renormalized quasilinear description. Thus, it is possible to close the ‘feedback loop’ of wave–ﬂow interactions, allowing a self-consistent analysis of the various system states, and enabling an understanding of the mechanisms and routes for bifurcation between them.

Of course, it is patently obvious that the zonal ﬂow problem is one of self-organization of a large structure in turbulence. Examples of other members of this class include transport barrier and proﬁle formation and dynamics, the origin of the solar differential rotation, the famous magnetic dynamo problem (relevant, in quite different limits, to the sun, earth, galaxy and reversed ﬁeld pinch), and the formation of proﬁles in turbulent and swirling pipe ﬂow. Table 1 summarizes these related structure formation phenomena, illustrating the objective of this review. Most of these problems are attacked at the simplest level by considering the stability of an ensemble or ‘gas’ of ambient turbulence to a seed perturbation. For example, in the dynamo problem, one starts by considering the stability of some state of magnetohydrodynamic (MHD) turbulence to a seed magnetic ﬁeld. In the zonal ﬂow problem, one correspondingly considers the stability of a gas of drift waves to a seed shear. The incidence of instability means that the initial vortex tilt will be re-enforced, thus amplifying the seed perturbation. It should be noted that the zonal ﬂow formation phenomenon is related to, but not quite the same as, the well-known inverse cascade of energy in a two-dimensional ﬂuid, which leads to large scale vortex formation. This is because the inverse cascade proceeds via a local coupling in wavenumber space, while zonal ﬂow generation occurs via non-local transfer of energy between small and large scales. Indeed, zonal shear ampliﬁcation is rather like the familiar α-effect from dynamo theory, which describes a non-local transfer of magnetic helicity to large scale. We also note that the initial stage of pattern formation instability meets only part of the challenge to a theoretical description of structure formation, and that one must subsequently ‘close the loop’ by understanding the mechanisms of saturation of the zonal ﬂow instability. The saturation of zonal ﬂows driven by drift wave turbulence is now a subject of intensive theoretical and computational investigation, worldwide.

As a related phenomena, convective cells have been subject to intensive study for a long time. The convective cell is a perturbation which is constant along the magnetic ﬁeld line but changes in the direction perpendicular to the magnetic ﬁeld. Such a structure is known to be induced by background drift wave turbulence. The zonal ﬂow can be considered as a particular example of an anisotropic convective cell. However, the convective cells of greatest interest as agents of transport are localized in the poloidal direction and extended radially, which is the opposite limit of anisotropy from that of the zonal ﬂow. Such cells are commonly referred to as streamers.

As the zonal ﬂow problem is a member of a large class of rapidly expanding research topics, the perspective of this review is composed as follows. First, we present detailed explanations of the physical understanding of drift wave–zonal ﬂow turbulence. Second, we also stress the view that studies on toroidal plasma turbulence enhance our understanding of turbulent structure formation in nature. In this sense, this review is a companion paper to recent reviews on the magnetic dynamo problem which, taken together, present a uniﬁed view that addresses the mystery of structure formation in turbulent media. Third, the impact of direct nonlinear simulation (DNS) is discussed in the context of understanding zonal ﬂow physics, although a survey of DNS techniques themselves is beyond the scope of this review. It is certainly the case that DNS studies have signiﬁcantly furthered our understanding of drift wave–zonal ﬂow turbulence. For these reasons, examples are mainly chosen from the realm of core plasma (i.e. drift wave) turbulence. In order to maintain transparency and to be concise, this review is limited in scope. Studies of edge turbulence and of general convective cell physics are not treated in depth here. While these topics are closely related to the topic of this review, extensive introductory discussions, which are too lengthy for this paper, are necessary. Hence, details of these important areas are left for future reviews.

翻译考点：
考点1：”zonal flow“必须译为”带状流“；
考点2：”drift waveturbulence transport“必须译为”漂移波湍流输运“；
考点3：”Reynolds stress“必须译为”雷诺应力“；
考点4：”inverse cascade of energy“必须译为”能量逆级联“；
考点5：”magnetohydrodynamic“必须译为”磁流体动力学“；
考点6：”azimuthally symmetric“必须译为”轴对称“；
考点7：”convective cells“必须译为”对流元“；
考点8：”Jovian belts“必须译为”木星云带“；
考点9：”regimes of drift wave turbulence“必须译为”漂移波湍流（参数）区域“；
考点10：”Rosenbluth“人名不推荐翻译为中文；
考点11：”underlying“推荐译为”潜在的“；
考点12：”streamers“必须译为”流带“；
考点13：”differ in an important way from“推荐译为”重要区别是“。