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.

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Zonal flows in plasma—a review

The understanding and predictive capability of transport physics and plasma confinement is reviewed from the perspective of achieving reactor-scale burning plasmas in the ITER tokamak, for both core and edge plasma regions. Very considerable progress has been made in understanding, controlling and predicting tokamak transport across a wide variety of plasma conditions and regimes since the publication of the ITER Physics Basis (IPB) document (1999 Nucl. Fusion 39 2137-2664). Major areas of progress considered here follow. (1) Substantial improvement in the physics content, capability and reliability of transport simulation and modelling codes, leading to much increased theory/experiment interaction as these codes are increasingly used to interpret and predict experiment. (2) Remarkable progress has been made in developing and understanding regimes of improved core confinement. Internal transport barriers and other forms of reduced core transport are now routinely obtained in all the leading tokamak devices worldwide. (3) The importance of controlling the H-mode edge pedestal is now generally recognized. Substantial progress has been made in extending high confinement H-mode operation to the Greenwald density, the demonstration of Type I ELM mitigation and control techniques and systematic explanation of Type I ELM stability. Theory-based predictive capability has also shown progress by integrating the plasma and neutral transport with MHD stability. (4) Transport projections to ITER are now made using three complementary approaches: empirical or global scaling, theory-based transport modelling and dimensionless parameter scaling (previously, empirical scaling was the dominant approach). For the ITER base case or the reference scenario of conventional ELMy H-mode operation, all three techniques predict that ITER will have sufficient confinement to meet its design target of Q = 10 operation, within similar uncertainties.

https://iopscience.iop.org/article/10.1088/0029-5515/47/6/S02/pdf

Chapter 2: Plasma confinement and transport

Techniques of theoretical analysis and numerical simulation are combined to produce a dynamical model of tropical cumulonimbus convection which features a close cooperation between the updraught and downdraught circulations. The cloud-scale dynamics determine the structure and transfer properties. Sub-cloud-scale transfer is unimportant. A steady-state dynamical model shows that the upshear or down-shear propagation speed, c, of a cumulonimbus cell relative to the mid-level flow is determined as a function of the convective available potential energy, CAPE, and weakly influenced by the windshear through a non-dimensional number, R, of the large-scale flow. This propagation speed is almost constant for a wide range of R, with c≃ 0.3CAPE, but only possible if R ≳ 2.8 (small shear). This contrasts with a previous result for another regime of convection, obtained by Moncrieff and Green (1972), if R ⩽ 1 (high shear). The transfer of momentum is distinctive and of large magnitude. The initiation and growth of the convective circulation represent an essentially nonlinear, finite-amplitude process, whose properties are closely related to the wind profile in the tropical atmosphere. The numerical simulations attain a quasi-steady state of a complex, three dimensional nature, basic features of which can be represented in terms of the steady-state analysis. Moreover, the outflow of the downdraught air is closely related to the attainment of a steady circulation and suggests a mechanism both for the maintenance and the eventual breakdown of the convective regime.

The dynamics and simulation of tropical cumulonimbus and squall lines

Hydrodynamic and hydromagnetic stability

Within the past decade, satellite pictures have shown persistent cloud patterns which indicate that the flow in the atmospheric planetary boundary layer is often organized into helical secondary circulations aligned parallel to the mean flow. Theory and observation agree that both convection in the presence of shear and the dynamic inflection point instabilities of the Ekman layer lead to these flow patterns. The observations and theory are reviewed with emphasis on the dynamics-dominated flow.

Longitudinal instabilities and secondary flows in the planetary boundary layer: A review

Small perturbations of plane Couette flow in stably and unstably stratified fluid are considered. It is found that the system is more unstable when it is bounded both above and below than when its depth is infinite, but a finite negative Richardson number J is required to maintain the perturbation for both cases. For the former case, this limiting Richardson number is −3k12/4(k12 + k22), while for the latter it is −2k12/(k12 + k12), where k1 and k2 are wavenumbers in the mean flow and the transversal direction. These results show that in an unstably stratified layer of Couette flow, the preferred mode of motion is roll‐type convection, with the dimension in the wind direction much larger than in the transversal direction. The amplification factor σ for the perturbations has been determined as a function of the modified Richardson number J = gSzUz−2(1 + k1−2k22), and the dimensionless wavenumber α = h(k12 + k12)1/2. Four different regimes have been found, each corresponding to a different type of perturbation. An application of the theory is made to the formation of longitudinal cloud rolls observed in the earth's atmosphere and in certain laboratory experiments.

H. L. Kuo

Papers

Perturbations of Plane Couette Flow in Stratified Fluid and Origin of Cloud Streets