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The current of a free mode included in a zonally elongated basin is zonal almost everywhere, with the exception of the westernmost and easternmost areas of the fluid domain. The main difference between different circulation fields basically concerns the latitudinal localisation of the maximum and minimum flow. This aspect is investigated by determining how total vorticity selects above localisations. The result is that the latter only depends on the value taken by the total vorticity at the points where the stream function is zero. A set of examples illustrates the results. [ABSTRACT FROM AUTHOR]

Two model calculations which elucidate the basic physics of zonal flow generation are presented. The first uses statistical ray optics to clarify the physics of the modulational instability process. The second uses the envelope formalism to obtain and solve a simple system of equations for the zonal flow and drift wave envelope. This simple system is closely analogous to the Zakharov equations for Langmuir turbulence.

The work presents the development of Rhines' theory for mixed topographic-planetary waves in a stratified ocean on a background current. The vertical anisotropy of baroclinic Rossby waves has been established depending on the slopes of the topography. If for positive slopes (water shallowing to the north) the baroclinic mode node shifts downward, then for negative slopes the frequency and phase velocity decrease and the vertical node shifts upward. Estimates of frequency variability for vertical modes at a negative bottom slope were obtained. For weak changes in bottom topography in the long-wave limit, an analytical asymptotic expression of the dispersion relation for the surface mode is constructed for positive and negative slopes. The dispersion curves in one-dimensional and two-dimensional cases were analyzed numerically. It is shown that the range of influence of topography on baroclinic waves reaches maximum deviations of the order of 50% in the long-wave part of the spectrum. [ABSTRACT FROM AUTHOR]

Abstract This paper presents a comparative study of zonal flow screening in positive and negative triangularity tokamaks. Neoclassical screening sets the strength of zonal flow shear for fixed drive and damping. Orbit calculations show that the radial excursions of trapped particles are reduced in negative triangularity tokamaks, as compared to positive triangularity. Yet surprisingly, the neoclassical dielectric susceptibility actually increases with decreasing triangularity, such that the susceptibility is higher for negative triangularity than for positive triangularity. This is because the reduction in neoclassical polarization by shrinking the banana width is offset by the increase in neoclassical polarization by the enhancement of trapped fraction for negative triangularity. As a result, the zonal flow screening length is actually enhanced for negative triangularity, as compared to positive triangularity. Hence, the zonal flow residual is smaller for negative triangularity than for positive triangularity. Results from gyrokinetic simulations support the analytic calculations.

Due to their huge socio-economic impacts and complex formation causes, extreme and continuous drought events have become the focus and nodus of research in recent years. In the midsummer (July–August) of 2022, a severe drought event occurred in the whole Yangtze River Basin (YRB), China. During that period, the precipitation in the upper, middle and lower reaches of the YRB dropped over 40% less than the 1961–2021 climatic mean, which had never happened previously. Furthermore, the temperature was the highest during 1961–2022. The record-breaking magnitude of less rainfall and high temperature directly led to the continuous development of this extreme drought event. An atmospheric moisture budget analysis revealed that the YRB midsummer rainfall anomaly was dominated by the anomalous powerful vertical moisture advection, which was derived from the strongest descending motion over the whole YRB in the 2022 midsummer during 1981–2022. The western Pacific subtropical high (WPSH) during the midsummer remained stronger, more westward and lasted longer than the climatic mean. As a result, the whole YRB was controlled by a positive geopotential height centre. Further evidence revealed that the anomalous subtropical zonal flow played a crucial role in inducing the extreme descent over the YRB. Moreover, the anomalous upper-tropospheric easterly flow over the YRB in 2022 is the strongest during 1981–2022, modulating the generation of the unprecedented descent anomaly over the YRB. The likelihood that an integrated connection of severe drought in East Asia and flood in West Asia and northwestern South Asia would increase when the extremely strong easterly anomalies in the upper troposphere emerged and induced descending adiabatic flow on the eastern sides of the Tibetan Plateau. The results of this study can provide scientific insights into the predictability of extreme drought events and provide ways to improve predictions.

The mutual interaction of drift wave-type modes and zonal flows causes the formation of higher-order nonlinear structures. This study focuses on the spatio-temporal behavior of these higher-order structures in a linear magnetized plasma. The structures include a solitary vortex, a long-lived circumnavigating motion localized both radially and azimuthally, and a short-lived packet of finer-scale fluctuations excited at the position of the solitary vortex. Observing the time evolution of the two-dimensional cross-sectional structures revealed that the packet of finer-scale fluctuations is trapped in the solitary vortex. The trapping times found are consistent with the theoretical evaluation. [ABSTRACT FROM AUTHOR]

In the summer (July and August) of 2022, unprecedented heat wave occurred along the Yangtze River Valley (YRV) over East Asia while unprecedented flood occurred over western South Asia (WSA), which are located on the eastern and western sides of Tibetan Plateau (TP). Here, by analyzing the interannual variability based on observational and reanalysis data, we show evidences that the anomalous zonal flow over subtropical Tibetan Plateau (TP) explains a major fraction the extreme events occurred in 2022. As isentropic surfaces incline eastward (westward) with altitude on the eastern (western) side of the warm center over TP in summer, anomalous easterly (westerly) flow in upper troposphere generates anomalous descent (ascent) on the eastern side of TP and anomalous ascent (descent) on the western side of TP via isentropic gliding. The anomalous easterly flow is extremely strong to reverse the climatological westerly flow over subtropical TP in 1994, 2006, 2013 and 2022. The easterly flow in 2022 is the strongest since 1979, and it generates unprecedented descent (ascent) anomaly on the eastern (western) side of TP, leading to extreme heat wave over YRV and extreme flood over WSA in 2022. The anomalously strong easterly flow over subtropical TP in 2022 is dominated by atmospheric internal variability related to mid-latitude wave train, while the cold sea surface temperature anomaly over the tropical Indian Ocean increases the probability of a reversed zonal flow over TP by reducing the meridional gradient of tropospheric temperature. [ABSTRACT FROM AUTHOR]

Two model calculations which elucidate the basic physics of zonal flow generation are presented. The first uses statistical ray optics to clarify the physics of the modulational instability process. The second uses the envelope formalism to obtain and solve a simple system of equations for the zonal flow and drift wave envelope. This simple system is closely analogous to the Zakharov equations for Langmuir turbulence.

A machine learning‐based semi‐empirical turbulent transport model DeKANIS has been modified to apply it independently of the device. DeKANIS predicts particle and heat fluxes, distinguishing diffusive and non‐diffusive transport processes. DeKANIS consists of a neural network (NN) model, which computes coefficients of the non‐diffusive terms and the ratio of the fluxes based on the gyrokinetic calculations, and a scaling formula, which estimates the turbulent saturation level founded on empirical fluxes. The datasets used for NN training have been prepared based on JT‐60U plasmas so far, but by exploiting JET plasmas, the datasets have been expanded and the parameter ranges covered by the NN models have become wider. The scaling formula has been rebuilt considering the decrease in the residual zonal flow level due to collisions. The new DeKANIS has demonstrated a reasonable profile prediction of an ITER plasma in the pre‐fusion power operation 1 phase with an integrated model GOTRESS+. In validating the prediction results with the gyrokinetic calculations, transport processes causing the fluxes have been exhibited. [ABSTRACT FROM AUTHOR]

We report an experimental study of the temperature and velocity fluctuations in supergravitational turbulent convection system. The negative spikes of the time series of temperature fluctuations appear periodically, which may result from the azimuthal movement of the cold plumes in the rotating frame pushed by the zonal flow. The period τ0 decreases slightly with increasing Rayleigh number (Ra) and τ0 is over one order larger than the time scale of the large-scale circulation. In addition, the temperature frequency power spectra follow P(f) ∼ f−5 for different Ra over the range 2 ≾ f ≾ 10, implying the possible existence of inverse cascade due to turbulence in equilibrium with zonal flow. The Rhines frequency fβ at which the inverse cascade ceases is around half of a decade smaller than the smallest frequency of the −5 scaling range. Further, the azimuthal distribution of the time-averaged radial velocity has no obvious peak and trough, which provides further evidence for the existence of zonal flow. Additionally, it is found that the probability density function for temperature and velocity fluctuations in the current system can be well fitted with the model (Wang et al. 2019, 2022) for the classical Rayleigh-Bénard convection. [ABSTRACT FROM AUTHOR]

The zonal flow and volume transport in the Luzon Strait play a crucial role in modulating the circulation, heat and material balance, and biogeochemical processes in the South China Sea (SCS), but the quantitative values remain unclear due to lack of long‐term direct observations. Here, this knowledge gap is bridged by analyzing 4‐year velocity measurements from a mooring array along 119.9°E. Based on the novel data, the mean value of the upper‐layer Luzon Strait transport (i.e., LST_up) is estimated at −4.54 ± 1.69 Sv. Seasonally, the westward LST_up attains its peak and trough in January and June with values of −6.80 ± 1.46 Sv and −2.59 ± 0.76 Sv, respectively. At the interannual time scale, the LST_up was strongest in 2016–2017 but weakest in 2017–2018. Further analysis suggested that local winds and the combination of local winds and upstream Kuroshio transport are likely the dominant modulation mechanisms for its seasonal and interannual variations, respectively. In the middle layer, a quasi‐steady cyclonic flow structure is identified and the volume transport is therefore trivial. We further found that seasonal variation of the middle‐layer transport is dominated by the eastward flow of this cyclonic structure. Corresponding to the gravest‐mode response in the Luzon Strait, seasonal‐to‐interannual variations of this middle‐layer eastward flow are nearly in‐phase with the upper‐layer westward flow. Overall, the above observational results provide a benchmark for the flow and transport in the Luzon Strait which can help understand the dynamics of the SCS circulation and validate and improve regional numerical simulations. Plain Language Summary: The Luzon Strait is the main channel connecting the South China Sea (SCS) with the Pacific Ocean and the volume transport through the strait is crucial in regulating physical and biogeochemical processes in the SCS. However, given the sparsity of long‐term direct observations, the knowledge of zonal flow and transports is still poor. In this study, novel insights into the zonal flow and transport in the Luzon Strait are obtained based on 4‐year velocity measurements from six moorings. The upper‐layer Luzon Strait transport is estimated at −4.54 ± 1.69 Sv (1 Sv = 106 m3 s−1; negative denotes westward). The flow in the middle layer presents a relatively steady cyclonic structure and the transport through the observed section is trivial because the westward and eastward flows cancel each other out. Seasonal‐to‐interannual variations of the transports are also analyzed. Further studies revealed that the middle‐layer eastward flow shows nearly the same phase with the upper‐layer westward flow at seasonal‐to‐interannual time scales. This corresponds well to the gravest‐mode response to external forcings. The present observed results will provide a benchmark for better understanding the dynamics of the SCS circulation and can be used to validate and improve numerical simulations in this region. Key Points: A quasi‐steady cyclonic flow structure is revealed in the middle layer of Luzon Strait based on 4‐year mooring observationsThe upper‐layer Luzon Strait transport is estimated at −4.54 ± 1.69 Sv while the middle‐layer transport is trivialThe upper‐layer westward flow and middle‐layer eastward flow show in‐phase temporal variations corresponding to the gravest‐mode response [ABSTRACT FROM AUTHOR]

This study employs gyrokinetic simulations to investigate ion temperature gradient (ITG) turbulence in realistic fusion reactor plasmas featuring reversed magnetic shear. The weakly negative magnetic shear is observed to be more stable for the ITG instability than strongly positive shear in this equilibrium configuration, primarily stemming from the scarcity of mode rational surfaces induced by the weak negative shear. This superiority in suppression for the negative shear persists in nonlinear turbulence with zonal flow artificially eliminated, where the emergence of turbulence solitons is observed and found associated with locally dense mode rational surfaces. However, the difference in transport levels among different magnetic shears diminishes in the presence of self-consistently generated zonal flow, accompanied by the disappearance of turbulence solitons. The nonlinear generation of zonal flow is found to be significantly affected by the magnetic shear. The study reveals a remarkable phenomenon that the Dimits shift no longer exists for negative magnetic shear, which is attributed to the weakness of the zonal flow generation near the ITG marginal stability.

Two-dimensional direct numerical simulations are performed to explore the effects of rough surfaces on the temperature fields, heat transport, and zonal flow in the annular centrifugal Rayleigh–Bénard convection (ACRBC) with cold inner and hot outer cylinders co-rotating axially, up to a Rayleigh number of Ra = 4.7 × 10 9. Three combinations of roughness are considered, that is, two rough surfaces (Case A), rough-inner/smooth-outer (Case B) and smooth-inner/rough-outer (Case C). It is shown that, the rough walls cause a bias in the temperature fields towards the values set on the rough walls at high Ra , while have a minimal impact at low Ra. This effect can be attributed to the rough walls promoting the generation and detachment of plumes, which act as the primary heat carriers in turbulent convective heat transfer. Furthermore, the presence of rough surfaces leads to enhanced heat transport at high Rayleigh numbers. Notably, two universal regimes are distinguished by the critical Rayleigh number R a c ≈ 1 0 9 : in regime I, where roughness elements protrude through the thermal boundary layer (BL), heat transport is significantly enhanced, resulting in a considerable increase in scaling exponent; in regime II, the scaling exponent reaches a saturation point, returning to a value similar to the smooth case. Similar findings are also observed in the classical Rayleigh–Bénard convection (Zhu et al., 2017). The decrease in scaling exponent can be attributed to the intense mixing caused by secondary vortices within the roughness elements, leading to a thin and uniformly distributed thermal BL along the rough surfaces, resembling the behavior observed in the smooth case. It is also found that roughness on the outer wall promotes the emergence of zonal flow, while roughness on the inner wall weakens it. These findings provide valuable insights into the effect of wall roughness on temperature fields, heat transport, and zonal flow in ACRBC. • The rough walls cause a bias in the temperature fields towards the values set on the rough walls at high Ra. • Two universal regimes are distinguished by the critical Rayleigh number R a c ≈ 1 0 9 . • Roughness on the outer wall promotes the emergence of zonal flow, while roughness on the inner wall weakens it. [ABSTRACT FROM AUTHOR]

The roles of wave phase structure and evolution in zonal flow dynamics are investigated. Previous work (Guo, Diamond; 2016) has noted that wave phase curvature is sufficient to produce a gradient in the Reynolds force and thus to drive zonal flow formation — even for turbulence of homogeneous fluctuation intensity. In this study, we investigate the energetics and nonlinear evolution of the process. For energetics, refraction (i.e. changes in phase gradient due to Z.F. shear) allows wave energy — and thus the ZF — to evolve at fixed wave amplitude. Using the phase evolution equation derived for the Hasegawa-Mima model, we prove energy conservation between waves and ZF, for fixed wave potential intensity. By separating the mesoscale phase into mean and fluctuation, we show that phase evolution induces ZF formation due to phase gradient shocks. Then, we investigate how linear and nonlinear feedback of the gradient affect the synchronization of the shock structure. Finally, we consider dynamic amplitude to explore the full predator-prey relationship between ZF (predator) and drift waves (prey).

The dynamics of solar tachocline is of importance in the solar magnetic activity; the underlying physics of tachocline dynamics, however, remains unclear. Studies of tachocline have shown that the nonlinear interaction of Rossby waves— a process of inhomogeneous mixing of potential vorticity (PV)— forms a zonal jet, while a mean toroidal magnetic field (B-field) suppresses the zonal flow with a critical parameter proportional to B2/η, where η is the magnetic diffusivity (Tobias et al. 2007). Thus, the role of toroidal B-field is of significance in turbulence properties of the tachocline. As a simple model of an incompressible and stably stratified tachocline, we consider a rotating, two-dimensional model— β-plane— and examine the effect of a mean B-field on the PV mixing in the β-plane turbulence. We report an analytical theory of jet suppression due to the mean B-field, which also enters as a modification of the cross phase in the vorticity flux, and as an initiator for a flow along the tiled field lines. A mean field equation for the vorticity and comparisons of real-space and k-space formulations will also be presented by using closure and quasi-linear approximations.*This work is supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54738.

Proximity to the density limit is characterized by degraded particle confinement, rise in edge turbulence and collapse of zonal flows. We present extensive theoretical work (Hajjar et al. 2018, Phys. Plasmas 25, 062306) which shows that the key parameter governing the flow collapse transition is electron adiabaticity. We show that zonal flow production drops precipitously in the hydrodynamic electron regime, as thenon-diffusive vorticity flux (i.e. residual stress) declines in proportion to adiabaticity. A simple physical argument establishes that the familiar cartoon of zonal flow production by eddy tilting fails in the hydrodynamic regime, as there causality and Reynolds stress tend to decouple. We show that reduced zonal flow production is the mechanism for particle confinement degradation in L-mode, and present a feedback loop mechanism for the cooling front. Several associated experimental studies are suggested. We also discuss the density limit in H-mode and its relation to the H to L back transition. A key element here is the invasion of the edge by turbulence, which spreads from the SOL.This work is supported by the U.S. Department of Energy under Award No. DE-FG02-04ER54738.

We report a direct numerical simulation (DNS) study of the heat transport and temperature profiles of the plume ejecting and impacting regions in the two-dimensional turbulent Rayleigh–Bénard (RB) convection with slippery plates and horizontally periodic boundary conditions. The numerical study is conducted in the parameter range of Rayleigh number R a from 10 7 to 10 9 and the slip length b from 0 (NS) to ∞ (FS) for the top and bottom plates. Two distinct flow patterns can be seen depending on b, namely convection roll state and zonal flow, which affect the Nusselt number N u and the Reynolds number R e . We show that the zonal flow occurs when the normalised slip length b / λ 0 ≳ 20 , where λ 0 is the thermal boundary layer thickness for the no-slip (NS) plates. N u and R e increase with increasing b / λ 0 , and can reach the optimum before the generation of the zonal flow. It is observed that N u ∼ R a γ N u with the effective scaling exponent γ N u = 0.30 ± 0.01 for the convection roll state, and γ N u = 0.16 ± 0.01 for the zonal flow. Furthermore, for the convection roll state, the power-law scaling of the local heat flux is N u ∼ R a 0.33 in the plume ejecting region, while in the plume impacting region, N u ∼ R a 0.28 for varying slip length b / λ 0 . The DNS data with different slippery plates for both plume ejecting and impacting regions agree well with the predicted temperature profiles by Huang et al. (J Fluid Mech. 2022;943:A2). [ABSTRACT FROM AUTHOR]

The nonlocal eigenmode analysis of low-frequency zonal flows (ZFs) in toroidally rotating tokamak plasmas is performed in the framework of the reduced one-fluid ideal magnetohydrodynamic model. It is shown that for typical profiles of plasma parameters toroidal plasma rotation results in the global ZF formation on the periphery of plasma column. For some types of equilibria these ZFs are aperiodically unstable that leads to the excitation of the differential plasma rotation at the tokamak plasma edge. [ABSTRACT FROM AUTHOR]

Nonlinear excitation of low frequency zonal structure (LFZS) by beta-induced Alfvén eigenmode (BAE) is investigated using nonlinear gyrokinetic theory. It is found that electrostatic zonal flow (ZF), rather than zonal current, is preferentially excited by finite amplitude BAE. In addition to the well-known meso-scale radial envelope structure, ZF is also found to exhibit fine radial structure due to the localization of BAE with respect to mode rational surfaces. Specifically, the zonal electric field has an even mode structure at the rational surface where radial envelope peaks.

We report the results of the direct numerical simulations of two-dimensional Rayleigh-Bénard convection(RBC) in order to study the influence of the periodic (PD) and confined (CF) samples on the heat transport Nu. The numerical study is conducted with the Rayleigh number (Ra) varied in the range 106≤Ra≤109 at a fixed Prandtl number Pr=4.3 and aspect ratio Γ=2 with the no-slip (NS) and free-slip(FS) plates. There exists a zonal flow for Ra≥3×106 with the free-slip plates in the periodic sample. In all the other cases, the flow is the closed large-scale circulation (closed LSC). The striking features are that the heat transport Nu is influenced and the temperature profiles do not be influenced when the flow pattern is zonal flow.

This paper presents a mechanism for enhanced regulation of drift wave turbulence by zonal flows in the presence of a fast ion population. It demonstrates that dilution effects due to the energetic particles (EPs) have a far-reaching impact on all aspects of the nonlinear dynamics. The modulational growth of zonal flow shear and the corresponding evolution of drift wave energy are calculated with dilution effects. The coupled zonal flow growth and drift wave energy equations are reduced to a predator–prey model. This is solved for the fixed points, which represents the various states of the system. Results display a strong dependence on dilution, which leads to greatly reduced levels of saturated turbulence and transport. Implications for the FIRE mode plasma of KSTAR are discussed in detail. This model is perhaps the simplest dynamical one which captures the beneficial effects of EPs on confinement.

The turbulent transport properties and dynamics of zonal flows (ZFs) in the presence of fast ions (FIs) are investigated for a typical internal transport barrier (ITB) plasma based on the gyrokinetic approach, focusing on the role of FI temperature and the effects of the toroidal rotation, including the E × B rotational shear, parallel velocity gradient (PVG) as well as the rotation velocity itself. Linear GENE simulations have shown that the core ITB plasma on HL-2A is dominated by ion temperature gradient (ITG) modes and trapped electron modes (TEMs), where the former is stabilized by FIs whereas destabilized by the PVG. Neither of the FIs or the PVG has observable effect on TEMs. The ion heat transport generally decreases at large FI temperature due to the nonlinear electromagnetic stabilization of turbulence with increased total plasma β until electromagnetic modes are excited. The transport fluxes peak around a certain FI temperature and the ZF shearing rate is significantly higher at such value compared with that in the absence of FIs, and the heat flux reduction is a result of the synergistic interaction between turbulence, ZFs and the external rotational shear. The E × B shear stabilizing and PVG destabilizing is not obvious at low normalized ITG R / L _Ti , indicating they are less important in determining the stiffness level in the relatively low density and rotation scenarios regarding the HL-2A ITB discharges. The turbulence suppression is predominated by the nonlinear stabilization of ITG turbulence as well as enhanced ZFs simultaneously in the presence of FIs. These results have also provided the possible way to reduce the turbulence transport through increasing the FI temperature in the off-axis neutral beam heated plasmas such as in HL-2A.

The I-mode is a natural edge localized mode (ELM)-free regime with H-mode-like improved energy confinement and L-mode-like particle confinement, making it an attractive scenario for future tokamak-based fusion reactors. A kind of low-frequency oscillation has been widely observed, with a frequency between stationary zonal flow and geodesic-acoustic mode (GAM) zonal flow. In EAST, most stationary I-mode shots have such a mode, called edge temperature ring oscillation (ETRO). This mode probably plays an important role in development and maintenance of the I-mode , while investigations are needed to clarify the differences between ETRO and similar mode low-frequency oscillation in other devices, such as limit cycle oscillation (LCO). In this paper, the properties of ETRO are described in detail, including the structure of its magnetic components, its radial propagation characteristics, statistics of its central frequency, a linear analysis of the alternating transition turbulences and a comparison with GAM and LCO. Although some similarities can be found between ETRO and both GAM and LCO, the main features are not identical. ETRO is probably a novel type of finite frequency zonal flow or pressure gradient-induced drift that is unique to the I-mode. It is found that modest fueling can reduce ETRO intensity while maintaining I-mode confinement, suggesting that supersonic molecular beam injection could be used as an effective tool to control ETRO.

Turbulent transport and zonal flow (ZF) dynamics in the mixed kinetic ballooning mode (KBM) and ion temperature gradient (ITG) mode dominated turbulence states are analyzed by gyrokinetic simulations based on the experimental observations of KBMs in the HL-2A Internal Transport Barrier (ITB) plasmas with weak magnetic shear configuration. Results have shown that KBMs and ITGs are the main candidates for turbulent transport and the inclusion of fast ions (FIs) can destabilize both instabilities, which is resulted by the decrease of ballooning parameter α _MHD hence reduced Shafranov shift stabilization due to the negative FI density gradient, making them more unstable according to the ŝ-α _MHD diagram. In addition, the ITGs are suppressed by both dilution and finite- β stabilization effects caused by FIs. Nonlinear simulations excluding the effects of FIs indicate that the transport is minimum at ${\beta _e} = \beta _e^{\exp }$ as the turbulence predominated by ITGs is strongly suppressed by the nonlinear electromagnetic (EM) stabilization and enhancement of ZFs. However, the transport is further increased with β _e although the ZFs become stronger due to the transition from ITG to KBM dominated turbulence state. The presence of FIs can modify the relation between ZF shearing rate and β _e . The transport level is insensitive to β _e when ${\beta _{\text{e}}} \unicode{x2A7D} \beta _{\text{e}}^{\exp }$ but increases significantly because of the KBM destabilization. Meanwhile, the ZF amplitude reaches maximum at ${\beta _{\text{e}}} = \beta _{\text{e}}^{\exp }$ whereas it suffers an erosion at higher values, implying that the plasma might be a self-organized critical state owning to the interactions among ZFs, KBMs and FI effects hence setting the plasma β around β ^exp . The results have also provided a possible explanation that the destabilization of EM turbulence is responsible for the ion heat transport stiffness under weak magnetic shear configurations in the off-axis neutral beam injection heated ITB plasmas on HL-2A.

The onset of turbulent heat transport at a higher temperature gradient than the critical gradient of linear instability, known as the Dimits shift, is a recurring feature of nonlinear simulations for magnetically confined fusion plasmas. Resonance in the nonlinear coupling between the modes that dominate energy transfer can lead to suppression of turbulence and transport above the linear critical gradient. As an expression of this resonance, gyrokinetic simulations show a quasi-coherent interaction between streamers and sidebands coupled through the zonal flow within the Dimits regime. This mechanism is further confirmed by use of artificial complex frequencies which break the resonance. By incorporating corresponding saturation physics, the standard quasilinear model for rapid head flux prediction is improved, which can now predict reduced heat flux in the Dimits regime. In particular, the triplet correlation time, the lifetime of the nonlinear interaction, is shown to be well-approximated by combinations of linear eigenvalues, and yields good representations of the heat flux variation both in and above the Dimits regime. Thus, a reduced but predictive model for transport near the critical gradient of zonal-flow saturated turbulence now exists.

Linear and nonlinear simulations are carried out for the edge coherent mode (ECM) using the global gyrokinetic code GEM based on the EAST experimental parameters. The linear simulation results show that ECM is an electrostatic mode with dominant toroidal mode number n = 18 and frequency about 48 kHz, and propagates along the direction of electron diamagnetic drift, which are consistent with the experimental results. In addition, the density and electron temperature gradients destabilize the mode, while the collision stabilizes the mode. The nonlinear simulation results show that the saturated particle and heat fluxes induced by ECM are mainly due to the perturbed electrostatic ExB drift, and the fluxes of electrons and ions are almost equal. The ECM drives significant outward particle and heat fluxes, thus greatly promoting the maintenance of the long pulse H-mode. The Fourier decomposition of fluxes and potentials demonstrate that the intermediate- n modes of n = 14, 18 grow fastest in the linear phase, while in the nonlinear saturation phase, the low-n modes such as n = 4, 6 dominate and the fluxes are mainly contributed by the mode of n = 10. It is found that zonal flow is not the dominant saturation mechanism of the turbulence. The inverse spectral cascade of turbulence is inevitably observed in the nonlinear saturation process, indicating that it is a more universal turbulence saturation mechanism. It is also found that radial electric field can greatly reduce the turbulence intensity and transport level. From the analyses of frequency and transport channels, it can be concluded that ECM appears to be the collisionless trapped electron mode.

Based on first-principles nonlinear gyrokinetic simulations, the electrostatic turbulence properties in the internal transport barrier (ITB) region of an Experimental Advanced Superconducting Tokamak discharge (#93890) are investigated. Specifically, ITBs with steep density and temperature gradients are located in the weakly negative magnetic shear region at the plasma center. In the linear stage, the growth rate and frequency of the ion temperature gradient (ITG) mode increase significantly due to resonant excitation by trapped electrons. That is, the resonance between trapped electrons and the ITG becomes strong due to the precession drift reversal of trapped electrons by the negative magnetic shear and Shafranov shift. Meanwhile, the trapped electron mode is stable in the ITB region due to only a very small fraction of electrons precessing in the direction of the electron diamagnetic drift. Nonlinear simulations show that, after considering the non-adiabatic effect of trapped electrons, the heat conductivity of ions and the turbulence intensity increase by at least a factor of 7 compared with the results only considering the adiabatic effect of electrons. The zonal charge density of trapped electrons can partially cancel that of ions, which weakens the intensity of the zonal flow, and consequently reduces the zonal flow regulation and enhances the turbulent transport.

Transitions of tokamak confinement regimes from low- to high-confinement are studied on Alcator C-Mod (Hutchinson et al 1994 Phys. Plasmas 1 1511) tokamak using gas-puff-imaging, with a focus on the interaction between the edge drift-turbulence and the local shear flow. Results show that the nonlinear turbulent kinetic energy transfer rate into the shear flow becomes comparable to the estimated value of the drift turbulence growth rate at the time the turbulent kinetic energy starts to drop, leading to a net energy transfer that is comparable to the observed turbulence losses. A corresponding growth is observed in the shear flow kinetic energy. The above behavior is demonstrated across a series of experiments. Thus both the drive of the edge zonal flow and the initial reduction of turbulence fluctuation power are shown to be consistent with a lossless kinetic energy conversion mechanism, which consequently mediates the transition into H-mode. The edge pressure gradient is then observed to build on a slower (1ms) timescale, locking in the H-mode state. These results unambiguously establish the time sequence of the transition as: first the peaking of the normalized Reynolds power, then the collapse of the turbulence, and finally the rise of the diamagnetic electric field shear as the L-H transition occurs. © 2014 IOP Publishing Ltd.

The intermediate oscillatory phase during the L-H transition, termed the I-phase, is studied in the EAST superconducting tokamak using a newly developed dual gas puff imaging (GPI) system near the L-H transition power threshold. The experimental observations suggest that the oscillatory behaviour appearing at the L-H transition could be induced by the synergistic effect of the two components of the sheared m, n = 0 E × B flow, i.e. the turbulence-driven zonal flow (ZF) and the equilibrium flow. The latter arises from the equilibrium, and is, to leading order, balanced by the ion diamagnetic term in the radial force balance equation. A slow increase in the poloidal flow and its shear at the plasma edge are observed tens of milliseconds prior to the I-phase. During the I-phase, the turbulence recovery appears to originate from the vicinity of the separatrix with clear wave fronts propagating both outwards into the far scrape-off layer (SOL) and inwards into the core plasma. The turbulence Reynolds stress is directly measured using the GPI system during the I-phase, providing direct evidence of kinetic energy transfer from turbulence to ZFs at the plasma edge. The GPI observations strongly suggest that the SOL transport physics and the evolution of pressure gradient near the separatrix play an important role in the L-I-H transition dynamics. To highlight these new physics, the previous predator-prey model is extended to include a new equation for the SOL physics. The model successfully reproduces the L-I-H transition process with several features comparing favourably with GPI observations. © 2014 IAEA, Vienna.

Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core-mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigid mantle and the underlying low viscosity fluid. The present experimental study investigates the effect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (. Cébron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g., . Calkins et al., 2010; Sauret and Le Dizès, submitted for publication). © 2012 Elsevier B.V.

Forced longitudinal librations are oscillatory perturbations of the rotation rate of a planet resulting from a gravitational coupling with orbital partners. In the present study we report the first experimental evidence that a librating cylindrical container can viscously drive mean azimuthal flows in the liquid interior, hereafter referred to as zonal flows. Using a novel laser Doppler velocimetry system, the current work extends upon the study of libration-driven flows by Noir et al. (2009). We investigate the different mechanisms underlying the zonal flow generation. It is found that zonal flows in the interior result primarily from non-linearities in the Ekman boundary layer. Furthermore, the zonal flow scales as the square of the libration amplitude and is independent of the Ekman number. This scaling implies that forced longitudinal libration in an axisymmetric container (purely viscous coupling) will drive unobservably small zonal flows at planetary conditions. Thus, purely viscous librational coupling will not generate significant energy dissipation in a planetary fluid layer. It follows that any observed phase lag between the gravitational forcing and the orbital response of a planet requires non-viscous coupling mechanisms to account for the energy dissipation. © 2010 .

Spatiotemporal structures of fluctuations with frequencies lower than the ion cyclotron frequency in a cylindrical magnetized plasma are investigated. Drift-wave and low-frequency zonal flow coexist. Electrostatic potentials of the zonal flow and the drift-wave are distributed widely in radius. The radial wave number profile of the zonal flow has a shear structure at the radial location where the drift-wave has a maximal normalized fluctuation amplitude. On the other hand, the radial wave number profile of the drift-wave shows vortex tilting, resulting in the generation of stationary turbulence Reynolds stress gradient per mass density. The envelope and bispectral analyses indicate significant nonlinear interactions between the zonal flow and the drift-wave. ©2008 The Physical Society of Japan.

A major upgrade of the experimental device for quasi-2 dimensional turbulence studies in magnetized electrolyte system is presented. The development has been motivated by the preparation of envisaged new experiments to investigate the effect of boundary walls on 2D turbulence cascades and the study of small vortex interactions with large scale sheared flows. The latter problem is relevant in different basic scientific as well as applied areas such as the reduction of anomalous transport via shear flows in magnetically confined fusion plasmas. The hardware upgrade consists of: (a) significantly larger electrolyte tank able to accommodate up to 2500 permanent magnets and adjustable walls, (b) ensemble of an electronically driven solenoid and a configurable permanent magnet array, (c) highly automatic acquisition and control of the experimental data and parameters. A first experimental test of the upgraded device is also presented. [ABSTRACT FROM AUTHOR]

In order to describe the resistive drift wave turbulence appearing in nuclear fusion plasma, the Hasegawa-Wakatani (HW) equations were proposed in 1983. We consider the two-dimensional HW equations, which have numerous structures (that is, they explain the branching phenomenon in turbulent and zonal flow in a two-dimensional plasma) and the generalized HW equations that include temperature fluctuation. We prove the global-in-time existence of a unique strong solution to both the HW equations and the generalized HW equations in a two-dimensional domain with double periodic boundary conditions. [ABSTRACT FROM AUTHOR]

We formulate a statistical wave-mechanical approach to describe dissipation and instabilities in two-dimensional turbulent flows of magnetized plasmas and atmospheric fluids, such as drift and Rossby waves. This is made possible by the existence of Hilbert space, associated with the electric potential of plasma or stream function of atmospheric fluid. We therefore regard such turbulent flows as macroscopic wave-mechanical phenomena, driven by the non-Hermitian Hamiltonian operator we derive, whose anti-Hermitian component is attributed to an effect of the environment. Introducing a wave-mechanical density operator for the statistical ensembles of waves, we formulate master equations and define observables: such as the enstrophy and energy of both the waves and zonal flow as statistical averages. We establish that our open system can generally follow two types of time evolution, depending on whether the environment hinders or assists the system’s stability and integrity. We also consider a phase-space formulation of the theory, including the geometrical-optic limit and beyond, and study the conservation laws of physical observables. It is thus shown that the approach predicts various mechanisms of energy and enstrophy exchange between drift waves and zonal flow, which were hitherto overlooked in models based on wave kinetic equations.

Zonal flow vacillation with very long time scales is observed in a 3070-day simple GCM simulation with zonally symmetric forcing. The long lasting zonal wind anomalies suggest that zonal flow vacillation is self-maintained. Wave-mean flow interactions are investigated by composite analysis and transform Eulerian momentum budget analysis. Nonlinear life-cycle simulations are conducted to demonstrate that each extreme phase of the zonal flow vacillation is a quasi stable state and is self-maintained by the embedded synoptic eddies.The firm EOF mode of zonal-mean wind shows an out of phase relation between anomalies at 60°S and at 40°S with a barotropic structure. This structure is similar to the dominant vacillation pattern observed in the Southern Hemisphere. The composite jet stream in the high (low) index phase of zonal flow vacillation shifts poleward (equatorward) from the time-mean location and becomes broader (narrower) and weaker (stronger). Composite eddies in the high index Phase tilt NW-SE and show mostly equatorward propagation, while eddies in the low index phase have “banana” shapes and propagate both equatorward and poleward. Transformed Eulerian momentum budget analyses show that the differences of wave propagation between two extreme phases result in the anomalous eddy forcing needed to maintain zonal wind anomalies against frictional damping.Budget analyses also indicate that eddy momentum flux convergence is the major positive forcing in both the extreme and transition phases. Eddy baroclinic forcing exerts weak damping on the wind anomalies in the upper troposphere but acts together with residual circulation forcing to counteract frictional damping near the surface. The major balance during the index cycle is between eddy barotropic forcing and residual circulation forcing in the upper troposphere and between residual circulation forcing and frictional damping in the lower troposphere. Further comparisons of eddy forcing from various time-scale eddies show that the anomalous eddy forcing is primarily provided by synoptic time scales. Two nonlinear life-cycle simulations, started separately from the composite zonal flows of the two extreme phases and small-amplitude wavenumber 6 perturbations, display the intensification of initial wind anomalies by the growing eddies. A dual-jet stream structure appears in the life-cycle simulation started from the high index composite, and a more intense single jet stream structure evolves from the low index initial state.It is noticed that maximum wind anomalies are established earlier at higher latitudes than at lower latitudes. This suggests that the mechanisms triggering transitions from one self-maintained phase to the other operate at higher latitudes. It is suspected that barotropic instability/stability is a possible triggering mechanism for transition from one state to another.