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Field-reversed configuration (FRC) is one of the approaches to realizing magnetic fusion due to its engineering simplicity. The recent C2-W experiment showed long-lasting FRC plasmas over 30 ms, with the help of neutral beam injection (NBI) and edge-biasing system. Therefore, understanding the edge-biasing effects on the FRC can be essential to improve the FRC designs and enable the potential active controls. The penetration of the edge biasing applied at the divertor ends can affect the equilibrium potential structure in the scrape-off layer (SOL) of FRC. The first part of the thesis is to establish a formulation that accurately captures both parallel and radial variations of the 2D potential in the SOL under the influence of edge-biasing. A full-f gyrokinetic ion model and a massless electron model are implemented in the GTC-X code to solve for the self-consistent equilibrium potential, given fixed radial potential profiles at the boundaries. Current simulation results implied that accurate electron density and temperature profiles are important in predicting the potential structure in the FRC SOL. The Debye sheath potential and the biasing profiles applied at the boundaries could introduce additional E×B rotation in the FRC SOL. With the equilibrium potential, the turbulent transport in the FRC can be modified due to the added E×B flow shear. Such shearing effects were first studied with an artificial 1D radial equilibrium potential for the ion temperature gradient (ITG) instability in the FRC SOL, which was identified as the dominant source for SOL fluctuations in the C2-W device. Linear δf simulations with adiabatic electrons found that the total shear from both the diamagnetic flow and the equilibrium E×B flow can reduce the linear growth rates and cause a radial tilting of the mode structures in the toroidal plane. Nonlinear simulations further confirmed that the flow shearing significantly decreases ITG saturation and ion heat transport levels. In addition, the self-generated zonal flow shears were also studied and played a similar role to reduce the ITG nonlinear saturation, unless the collisional damping limited the zonal flow level in the SOL. These results may suggest that using a proper edge-biasing profile and minimizing collisions could improve the confinement of the FRC. The full-f scheme developed in the 2D equilibrium simulation was aimed for coupled simulations of the turbulent transport with the self-consistent 2D equilibrium potential. As a starting point, this full-f algorithm had been compared with the δf simulations with periodic boundaries. Future research will involve the full-f simulations with the non-Maxwellian equilibrium distribution functions and open boundary flows in the FRC SOL.

Eddy saturation describes the nonlinear mechanism in geophysical flows whereby, when average conditions are considered, direct forcing of the zonal flow increases the eddy kinetic energy, while the energy associated with the zonal flow does not increase. We present a minimal baroclinic model that exhibits complete eddy saturation. Starting from Phillips’ classical quasi-geostrophic two-level model on the beta channel of the mid-latitudes, we derive a reduced order model comprising of six ordinary differential equations including parameterised eddies. This model features two physically realisable steady state solutions, one a purely zonal flow and one where, additionally, finite eddy motions are present. As the baroclinic forcing in the form of diabatic heating is increased, the zonal solution loses stability and the eddy solution becomes attracting. After this bifurcation, the zonal components of the solution are independent of the baroclinic forcing, and the excess of heat in the low latitudes is efficiently transported northwards by finite eddies, in the spirit of baroclinic adjustment.

We study differential rotation in late-stage shell convection in a 3D hydrodynamic simulation of a rapidly rotating $16M_\odot$ helium star with a particular focus on the convective oxygen shell. We find that the oxygen shell develops a quasi-stationary pattern of differential rotation that is neither described by uniform angular velocity as assumed in current stellar evolution models of supernova progenitors, nor by uniform specific angular momentum. Instead, the oxygen shell develops a positive angular velocity gradient with faster rotation at the equator than at the pole by tens of percent. We show that the angular momentum transport inside the convection zone is not adequately captured by a diffusive mixing-length flux proportional to the angular velocity or angular momentum gradient. Zonal flow averages reveal stable large-scale meridional flow and an entropy deficit near the equator that mirrors the patterns in the angular velocity. The structure of the flow is reminiscent of simulations of stellar surface convection zones and the differential rotation of the Sun, suggesting that similar effects are involved; future simulations will need to address in more detail how the interplay of buoyancy, inertial forces, and turbulent stresses shapes differential rotation during late-stage convection in massive stars. If convective regions develop positive angular velocity gradients, angular momentum could be shuffled out of the core region more efficiently, potentially making the formation of millisecond magnetars more difficult. Our findings have implications for neutron star birth spin periods and supernova explosion scenarios that involve rapid core rotation., 13 pages, 6 figures. Published in MNRAS

The high-precision Juno gravitational measurements allow us to infer the structure of Jupiter's deep atmospheric zonal flow. Since this inference is nonunique, it is important to explore the space of possible solutions. In this paper, we consider a model in which Jupiter's deep atmospheric zonal flow is barotropic, or invariant along the direction of the rotation axis, until it is truncated at depth by some dynamical process (e.g., Reynolds stress, Lorentz or viscous force). We calculate the density perturbation produced by the $z$-invariant part of the flow using the thermal wind equation and compare the associated odd zonal gravitational harmonics ($J_{3}$, $J_{5}$, $J_{7}$, $J_{9}$) to the Juno-derived values. Most of the antisymmetric gravitational signal measured by Juno can be explained by extending observed winds between $20.9^{\circ}\rm{S}-26.4^{\circ}\rm{N}$ to depths of $\sim 1000$ km. Because the small-scale features of the mid/high latitude zonal flow may not persist to depth, we allow the zonal flow in this region to differ from the observed surface winds. We find that the Juno odd zonal gravitational harmonics can be fully explained by $\sim 1000$ km deep barotropic zonal flows involving the observed winds between $20.9^{\circ}\rm{S}-26.4^{\circ}$N and a few broad mid/high latitude jets., Published in JGR: Planets

International audience; A model of E×B staircases is proposed, based on a wave kinetic equation coupled to a poloidal momentum equation. A staircase pattern is idealised as a periodic radial structure of zonal shear layers that bound regions of propagating wave packets, viewed as avalanches. Wave packets are trapped in shear flow layers due to refraction. In this model an E × B staircase motif emerges due to the interaction between propagating wave packets (avalanches) and trapped waves in presence of an instability drive. Amplitude, shape, and spatial period of the staircase E × B flow are predicted as functions of the background fluctuation spectrum and the growth rate of drift waves. The zonal flow velocity radial profile is found to peak near its maxima and to flatten near its minima. The optimum configuration for staircase formation is a growth rate that is maximum at zero radial wave number. A mean shear flow is responsible for a preferential propagation speed of avalanches. It is not a mandatory condition for the existence of staircase solutions, but has an impact on their spatial period.

We report on turbulent thermal convection experiments in a rotating cylinder with a diameter () to height () aspect ratio of. Using nitrogen and pressurised sulphur hexafluoride we cover Rayleigh numbers (Ra) from to at Prandtl numbers. For these Ra we measure the global vertical heat flux (i.e. the Nusselt number - Nu), as well as statistical quantities of local temperature measurements, as a function of the rotation rate, i.e. the inverse Rossby number - 1/Ro. In contrast to measurements in fluids with a higher Pr we do not find a heat transport enhancement, but only a decrease of Nu with increasing 1/Ro. When normalised with Nu(0) for the non-rotating system, data for all different Ra collapse and, for sufficiently large 1/Ro, follow a power law. Furthermore, we find that both the heat transport and the temperature field qualitatively change at rotation rates and. We interpret the first transition at as change from a large-scale circulation roll to the recently discovered boundary zonal flow (BZF). The second transition at rotation rate is not associated with a change of the flow morphology, but is rather the rotation rate for which the BZF is at its maximum. For faster rotation the vertical transport of warm and cold fluid near the sidewall within the BZF decreases and hence so does Nu.

A linear wave theory of the Rotating Shallow Water Equations (RSWE) is developed in a channel on either the mid-latitude f-plane/β-plane or on the equatorial β-plane in the presence of a uniform mean zonal flow that is balanced geostrophically by a meridional gradient of the fluid surface height. We show that this surface height gradient is a potential vorticity (PV) source that generates Rossby waves even on the f-plane similar to the generation of these waves by PV sources such as the β–effect, shear of the mean flow and bottom topography. Numerical solutions of the RSWE show that the resulting planetary (Rossby), Inertia-Gravity (Poincaré) and Kelvin-like waves differ from their counterparts without mean flow in both their phase speeds and meridional structures. Doppler shifting of the “no mean-flow” phase speeds does not account for the difference in phase speeds, and the meridional structure does not often oscillate across the channel but is trapped near one the channel's boundaries in mid latitudes or behaves as Hermite function in the case of an equatorial channel. The phase speed of Kelvin-like waves is modified by the presence of a mean flow compared to the classical gravity wave speed but their meridional velocity does not vanish. The gaps between the dispersion curves of adjacent Poincaré modes are not uniform but change with the zonal wavenumber, and the convexity of the dispersion curves also changes with the zonal wavenumber. In some cases, the Kelvin-like dispersion curve crosses those of Poincaré modes, but it is not an evidence for the existence of instability since the Kelvin waves are not part of the solutions of an eigenvalue problem.

In this work, we compare gyrokinetic simulations in stellarators using different computational domains, namely, flux tube, full-flux-surface, and radially global domains. Two problems are studied: the linear relaxation of zonal flows and the linear stability of ion temperature gradient (ITG) modes. Simulations are carried out with the codes EUTERPE, GENE, GENE-3D, and stella in magnetic configurations of LHD and W7-X using adiabatic electrons. The zonal flow relaxation properties obtained in different flux tubes are found to differ with each other and with the radially global result, except for sufficiently long flux tubes, in general. The flux tube length required for convergence is configuration-dependent. Similarly, for ITG instabilities, different flux tubes provide different results, but the discrepancy between them diminishes with increasing flux tube length. Full-flux-surface and flux tube simulations show good agreement in the calculation of the growth rate and frequency of the most unstable modes in LHD, while for W7-X differences in the growth rates are found between the flux tube and the full-flux-surface domains. Radially global simulations provide results close to the full-flux-surface ones. The radial scale of unstable ITG modes is studied in global and flux tube simulations finding that in W7-X, the radial scale of the most unstable modes depends on the binormal wavenumber, while in LHD no clear dependency is found., submitted to Nuclear Fusion

Near-resonant energy transfer to large-scale stable modes is shown to reduce transport above the linear critical gradient, contributing to the onset of transport at higher gradients. This is demonstrated for a threshold fluid theory of ion temperature gradient turbulence based on zonal-flow-catalyzed transfer. The heat flux is suppressed above the critical gradient by resonance in the triplet correlation time, a condition enforced by the wave numbers of the interaction of the unstable mode, zonal flow, and stable mode.

Turbulent thermal convection driven by a temperature difference is omnipresent in nature and it plays an important role in numerous industrial applications. Rayleigh-Benard convection (RBC) where a fluid layer in a cavity heated from below and cooled from above, is a classical model problem for the study of thermal convection. Another model problem is vertical convection (VC) where the fluid layer is heated/cooled at the sides. Both RBC and VC can be viewed as extreme cases of tilted convection where the tilt angle is 0° for RBC and 90° for VC. This thesis studies the above three model problems for thermal convection, i.e. Rayleigh-Benard convection (Part I), tilted convection (Part II), and vertical convection (Part III). In Part I, we study non-Oberbeck-Boussinesq (NOB) effects either due to density maximum of cold water near 4℃ (Chap. 2) or due to large temperature differences (Chap. 3) in turbulent RBC. We also investigate multistability of convection roll states (Chap. 4) and metastability of the zonal flow (Chap. 5) in turbulent RBC. In Part II, we focus on tilted convection. We report that tilting can promote flow reversals in a two-dimensional convection cell with aspect ratio 2 (Chap. 6). The global flow organization and heat transport for two-dimensional tilted convection with small aspect ratio 0.5 (Chap. 7) and large aspect ratios (Chap. 8) are also discussed. We further study NOB effects in three-dimensional tilted convection in Chap. 9. In Part III, we investigate vertical convection, and we particularly focus on NOB effects in two-dimensional vertical convection in Chap. 10.

The variability of the zonal-mean large-scale extratropical circulation is often studied using individual modes obtained from empirical orthogonal function (EOF) analyses. The prevailing reduced-order model of the leading EOF (EOF1) of zonal-mean zonal wind, called the annular mode, consists of an eddy–mean flow interaction mechanism that results in a positive feedback of EOF1 onto itself. However, a few studies have pointed out that under some circumstances in observations and GCMs, strong couplings exist between EOF1 and EOF2 at some lag times, resulting in decaying-oscillatory, or propagating, annular modes. Here, we introduce a reduced-order model for coupled EOF1 and EOF2 that accounts for potential cross-EOF eddy–zonal flow feedbacks. Using the analytical solution of this model, we derive conditions for the existence of the propagating regime based on the feedback strengths. Using this model, and idealized GCMs and stochastic prototypes, we show that cross-EOF feedbacks play an important role in controlling the persistence of the annular modes by setting the frequency of the oscillation. We find that stronger cross-EOF feedbacks lead to less persistent annular modes. Applying the coupled-EOF model to the Southern Hemisphere reanalysis data shows the existence of strong cross-EOF feedbacks. The results highlight the importance of considering the coupling of EOFs and cross-EOF feedbacks to fully understand the natural and forced variability of the zonal-mean large-scale circulation.

A series of experiments with rotating, electromagnetically forced, turbulent flows were carried out at the Sapienza University of Rome to investigate the eddy–wave duality in flows with a β-effect and the electromagnetic force acting in the westward direction. When the β-effect is significant, i.e., as in planetary atmospheric and oceanic circulations, nonlinear eddy/wave interactions facilitate flow self-organization into zonal patterns in which Rossby waves and westward propagating cyclonic and anticyclonic eddies coexist. Upon time averaging, eddies disappear and the flow pattern transforms into a system of alternating zonal jets. What is the relationship between eddies, jets, and Rossby waves? To address this issue, we designed a laboratory experiment in which a westward zonal flow is produced by applying an electro-magnetic small-scale forcing to a thin layer of a rotating fluid. In order to investigate different levels of flow zonality and a wider range of zonal modes, we varied the forcing intensity and the area of the forced sector. The zonal flow evolves as a system of westward propagating, large scale, cyclonic, and anticyclonic eddies. The propagation speed of the traveling structures was calculated from the Hovmöller diagrams of both the streamfunction and the centroids of clusters of different types (cyclonic and anticyclonic eddy cores and saddle point neighborhoods) obtained via an Okubo–Weiss analysis. The results were compared with the theoretical phase speed of a Rossby wave. The correspondence between these two characteristics at the radius of maximum shear corresponding to the epicenter of the barotropic instability is quite good, particularly after including the radial variation of the zonal velocity in the β-term. It is concluded that the Rossby waves and eddies are inseparable as the former maintain the instability that sustains the latter. This symbiosis visually resembles the Rossby soliton.

We studied the dynamics of the solar atmosphere in the region of a large quiet-Sun filament, which erupted on 21 October 2010. The filament eruption started at its northern end and disappeared from the H$\alpha$ line-core filtergrams line within a few hours. The very fast motions of the northern leg were recorded in ultraviolet light by AIA. We aim to study a wide range of available datasets describing the dynamics of the solar atmosphere for five days around the filament eruption. This interval covers three days of the filament evolution, one day before the filament growth and one day after the eruption. We search for possible triggers that lead to the eruption of the filament. The surface velocity field in the region of the filament were measured by means of time-distance helioseismology and coherent structure tracking. The apparent velocities in the higher atmosphere were estimated by tracking the features in the 30.4 nm AIA observations. To capture the evolution of the magnetic field, we extrapolated the photospheric line-of-sight magnetograms and also computed the decay index of the magnetic field. We found that photospheric velocity fields showed some peculiarities. Before the filament activation, we observed a temporal increase of the converging flows towards the filament's spine. In addition, the mean squared velocity increased temporarily before the activation and peaked just before it, followed by a steep decrease. We further see an increase in the average shear of the zonal flow component in the filament's region, followed by a steep decrease. The photospheric l.o.s. magnetic field shows a persistent increase of induction eastward from the filament spine. The decay index of the magnetic field at heights around 10 Mm shows a value larger than critical at the connecting point of the northern filament end., Comment: 11 pages, 12 figures, accepted for publication in Astronomy & Astrophysics

For rapidly rotating turbulent Rayleigh--B\'enard convection in a slender cylindrical cell, experiments and direct numerical simulations reveal a boundary zonal flow (BZF) that replaces the classical large-scale circulation. The BZF is located near the vertical side wall and enables enhanced heat transport there. Although the azimuthal velocity of the BZF is cyclonic (in the rotating frame), the temperature is an anticyclonic traveling wave of mode one whose signature is a bimodal temperature distribution near the radial boundary. The BZF width is found to scale like $Ra^{1/4}Ek^{2/3}$ where the Ekman number $Ek$ decreases with increasing rotation rate.

Recent studies found that atmospheric superrotation (i.e., west-to-east winds over the equator) on tidally locked planets can modify the phase of planetary waves. But, a clear relationship between the superrotation and the magnitude of the phase shift was not examined. In this study, we re-investigate this problem using a two-dimensional (2D) linear shallow water model with a specified uniform zonal flow. We find that the degree of the phase shift is a monotonic but nonlinear function of the strength of the mean flow, and the phase shift has two limits of -$\pi$ and +$\pi$. The existence of these limits can be explained using the energy balance of the whole system. We further show that a resonance between the Rossby wave and the mean flow occurs when the speed of an eastward jet approaches to the westward phase speed of the Rossby wave, or a resonance between the Kelvin wave and the mean flow happens when the speed of a westward jet approaches to the eastward phase speed of the Kelvin wave. The resonance mechanism is the same as that found in the previous studies on Earth and hot Jupiters. Moreover, in the spin-up period of a 3D global atmospheric general circulation simulation for tidally locked rocky planet, we also find these two phenomena: phase shift and wave--jet resonance. This study improves the understanding of wave--mean flow interactions on tidally locked planets.

Despite observational evidence of a distinct regime behaviour in the low-frequency variability of the North Atlantic Oscillation (NAO), the theoretical support for the existence of separate NAO regimes has been limited. Although NAO-like regimes have been detected in numerical models of varying complexity, the role of forcings and feedbacks originated by diabatic processes in the specific geographical setting of the North Atlantic region has not been explicitly advocated as a source of regime behaviour for the NAO. In this study, we develop a minimal theoretical model of the interactions between zonal flow (and associated temperature gradient), planetary waves and surface heat fluxes in the North Atlantic, guided by results from observational diagnostics. Using re-analysis data, we show that interactions between an equivalent barotropic NAO anomaly and climatological stationary waves with a baroclinic structure and a larger meridional scale generate a positive feedback between the NAO-like wave and the strength of the zonal flow. On the other hand, an increased zonal wind generates stronger surface heat fluxes which damp both the zonal and the wave components of the NAO-like anomaly. Using these observational results to guide the choice of empirical parameters, we construct a 3-variable model which is formally equivalent to the Lorenz (J Atmos Sci 20:130–141, 1963) chaotic model for Rayleigh–Benard convection, and possesses two regimes originated by oscillations around two weakly unstable stationary states. From a physical point of view, the two regimes correspond to opposite phases of a near-resonant planetary wave which occur when the zonal flow is either below (negative NAO) or above (positive NAO) the value corresponding to zero phase speed. Finally, we expand the model to a five-variable system by splitting the zonal-mean wind into its barotropic (i.e. height independent) and thermal component, and including a variable representing the area-averaged amplitude of high-frequency baroclinic eddies. Following earlier studies, we assume that high-frequency eddy activity grows by extracting available potential energy from the zonal-mean temperature gradient and decays by feeding kinetic energy into the barotropic component of the zonal wind. The extended model still displays a chaotic, two-regime behaviour, with additional sub-seasonal variability driven by the energy exchanges associated with high-frequency eddy amplification and decay.

International audience; Jupiter’s atmosphere is rotating differentially, with zones and belts rotating at speeds that differ by up to 100 metres per second. Whether this is also true of the gas giant’s interior has been unknown1,2, limiting our ability to probe the structure and composition of the planet3,4. The discovery by the Juno spacecraft that Jupiter’s gravity field is north–south asymmetric5 and the determination of its non-zero odd gravitational harmonics J3, J5, J7 and J9 demonstrates that the observed zonal cloud flow must persist to a depth of about 3,000 kilometres from the cloud tops6. Here we report an analysis of Jupiter’s even gravitational harmonics J4, J6, J8 and J10 as observed by Juno5 and compared to the predictions of interior models. We find that the deep interior of the planet rotates nearly as a rigid body, with differential rotation decreasing by at least an order of magnitude compared to the atmosphere. Moreover, we find that the atmospheric zonal flow extends to more than 2,000 kilometres and to less than 3,500 kilometres, making it fully consistent with the constraints obtained independently from the odd gravitational harmonics. This depth corresponds to the point at which the electric conductivity becomes large and magnetic drag should suppress differential rotation7. Given that electric conductivity is dependent on planetary mass, we expect the outer, differentially rotating region to be at least three times deeper in Saturn and to be shallower in massive giant planets and brown dwarfs.

Building on the work of Kravtsov and Reznik [J. Fluid Mech. 909, A23 (2021); hereafter KR21], we studied the interactions of a localized monopole with a rectilinear, constant-shear flow in a 1½-layer, f-plane, quasi-geostrophic model. The non-invariance of this model with respect to Galilean transformations plays a crucial role in the dynamics of such interactions. Of particular importance here are two configurations in which the center of the vortex is located on the line of zero zonal current and remains motionless in the background of a nonstationary flow field generated via interactions of the vortex with the zonal flow. In configuration I (II), the vortex is prograde (retrograde), that is, its vorticity is of the same (opposite) sign with the vorticity of the background flow. Configuration I is stable, whereas configuration II eventually breaks down: a retrograde vortex drifts off of the zero-current line, rapidly accelerates and radiates intense Rossby waves, which results in a gradual weakening of the vortex. Naturally, the same scenario plays out if a retrograde vortex is initially off of the zero-current line. On the other hand, a prograde vortex initially located at some distance from the zero-current line drifts toward this line, albeit at a rate that decreases with time, so the solution always tends to configuration I. Therefore, the line of zero zonal current “attracts” prograde vortices and “repels” retrograde vortices. The present numerical experiments with singular vortices, using the scheme developed in KR21, confirm the above scenarios and clarify their dynamics.

The verification and calibration of a new quasi-linear transport model with a large database of gyrokinetic turbulence simulations is presented in this paper. In a previous paper \cite{staebler:2020}, a model for the saturated spectrum of electric potential fluctuations was developed based on the properties of the non-linear 3D spectrum. In this paper, a modification to the overall multiplicative factor in this model is found to be necessary to improve the fit to scans of the temperature and density gradients and safety factor. The error in the fit of the quasi-linear fluxes of electron and ion energy fluxes is significantly better than for previous saturation models. The spectral shift model for the impact of equilibrium $E\times B$ velocity shear \cite{staebler:2013a} and the zonal flow mixing model for electron-scale turbulence \cite{staebler:2016} are both revised to be compatible with this new model. The models for the loss of bounce averaging and electron collisions in the TGLF reduced linear equations \cite{staebler:2005} are also changed to improve the linear eigenmodes.

Fluid flow excited by a core oscillating in a rotating spherical cavity is experimentally investigated. Oscillations are set by an external inertial field so that in the reference frame of the cavity, the core moves along a circular trajectory around the rotation axis. Two situations are considered: when the core oscillations are co-directed or counter-directed with respect to the rotation of the cavity. The oscillating core is a source of non-axisymmetric inertial waves that form a system of cone-shaped shear layers in fluid bulk. Depending on the oscillation frequency, various inertial flow regimes arise, the spatial structure of which strongly depends on the sign of the oscillations. It is found that a strong non-linear response in the form of a steady zonal flow corresponds to each flow regime. The flow structure is a system of nested liquid geostrophic cylinders, one of which is associated with the critical latitude at the core boundary, where inertial waves are generated. The next one is associated with the wave reflection from the cavity boundary and is clearly manifested when they are focused on the wave attractor. The most intense zonal flow occurs when inertial waves are superposed and global vortex structures are resonantly excited.

Interaction between a train of transient waves and a diffluent westerly jet is examined using a regional quasigeostrophic equivalent barotropic model with a (nearly) binary potential vorticity (PV) distribution. Unlike most previous studies, but consistent with the observed extratropical tropopause, cross-stream variation in the layer thickness is allowed to contribute to the discontinuity in PV. In all cases examined, short (i.e., barotropic) edge waves are continuously forced in the upstream, then migrate downstream, and eventually exit the domain. A quasilinear 1D theory based on the conservation of local wave activity predicts that no steady wave train can be maintained where the westerly zonal flow is decelerated below one-half of the initial value, at which point the wave envelope develops a migratory shock analogous to the Lighthill–Whitham–Richards traffic flow problem. Fully nonlinear high-resolution 2D calculations show that the wave train indeed undergoes a significant transformation once the zonal flow along the jet axis is decelerated below the threshold. The subsequent flow evolution depends on the nature of the discontinuity in the basic-state PV. When the discontinuity is entirely due to the vorticity profile, waves are compressed and partially deflected sideways but no complete blocking occurs. When the discontinuity in PV is augmented by the layer thickness variation, the incident wave train is blocked and split into two tracks at the stagnation point, eventually leading to a formation of a modon-like vortex pair, reminiscent of an atmospheric blocking. Implications for low-frequency variability of the atmosphere are discussed.

The response of the nonlinear shallow-water equations (SWE) on a sphere to tropical vorticity forcing is examined, with an emphasis on momentum fluxes and the emergence of a superrotating state. Fixing the radiative damping and momentum drag time-scales to be of the order of a few days, a state of superrotation (SR) is shown to emerge under steady large-scale and random small-scale vorticity forcing. In the first example, the stationary response to a pair of equal and oppositely signed vortices placed on the Equator is considered. Here, the equatorial flux budget is dominated by the eddy fluxes and these drive the system into a state of SR. Eventually, the flux associated with the momentum drag increases to balance the eddy fluxes, resulting in a steady state with a superrotating jet at the Equator. The initial value problem with these twin vortices also exhibits SR driven by eddy fluxes. Curiously, this transient solution spontaneously propagates westward and continually circumnavigates the globe. It is worth emphasizing that this SR state does not rely on any particular form of dissipation at large scales and is, in fact, observed even in the absence of any large-scale damping mechanism. In the second example, a random small-scale vorticity forcing is applied across the Tropics. The statistically steady state obtained is fairly turbulent in nature, but here too the eddy fluxes dominate and the system exhibits SR. It is important to note that, in both these cases, the direct forcing of the zonal mean zonal flow is zero by construction and the eddy fluxes at the Equator are responsible for its eastward acceleration. Further, in both these examples, the rotational part of the flow dominates the momentum fluxes as well as the stationary zonal mean zonal flow itself. Arguments based on the nature of potential vorticity and enstrophy are put forth to shed some light on these results.

International audience; We address the mechanisms underlying low-frequency zonal flow generation in a turbulent system through the parametric decay of collisionless trapped particle modes and its feedback on the stabilization of the system. This model is in connection with the observation of barrier transport in reduced gyrokinetic simulations (A. Ghizzo et al., Euro. Phys. Lett. 119(1), 15003 (2017)). Here the analysis is extended with a detailed description of the resonant mechanism. A key role is also played by an initial polarisation source that allows the emergence of strong initial shear flow. The parametric decay leads to the growth of a zonal flow which differs from the standard zero frequency zonal flow usually triggered by the Reynolds stress in fluid drift-wave turbulence. The resulting zonal flow can oscillate at low frequency close to the ion precession frequency, making it sensitive to strong amplification by resonant kinetic processes. The system becomes then intermittent. These new findings, obtained from numerical experiments based on reduced semi-Lagrangian gyrokinetic simulations, shed light on the underlying physics coming from resonant wave-particle interactions for the formation of transport barriers. Numerical simulations are based on a Hamiltonian reduction technique, including magnetic curvature and interchange turbulence, where both fastest scales (cyclotron and bounce motions) are gyro-averaged.

Nonlinear interaction of magnetized Rossby waves with sheared zonal flow in the Earth's ionospheric E-layer is investigated. It is shown that in case of weak nonlinearity 2D Charney vorticity equation can be reduced to the one-dimensional modified KdV equation. (C) 2019 Elsevier B.V. All rights reserved.

In conjunction with thermo-solutal convection, the turbulence generated in planetary liquid cores may be due to the role of boundary forcing through geophysically relevant mechanisms such as precession, libration and tidal forcing (Le Bars et al. 2015). In this paper, we discuss laboratory equatorial velocity measurements and selected high-resolution numerical simulations to show the generation of developed turbulence driven by longitudinal libration or tidal forcing. In both cases, the transition to saturated turbulence is driven by an elliptical instability that excites inertial modes of the system. We find striking similarities in both the transition to bulk turbulence and the enhanced zonal flow hinting at a generic fluid response independent of the forcing mechanism. We finally discuss the relevance of this work to the planetary regime and possible directions for future investigations.

The interaction of the drift wave (DW) turbulence and zonal flow (ZF) is investigated with the modified Hasegawa–Mima equation taking into account the backreaction of ZF velocity on DW turbulence. It is shown that the y-averaged enstrophy of DW turbulence and the velocity of ZF are intrinsically related. By utilizing this feature, a nonlinear stage of DW modulational instability is considered within the framework of the wave kinetic equation. It is shown that in this approximation, the nonlinear stage of the modulational instability results in the collapsing solutions, accompanied by the “wave breaking” phenomenon. Numerical simulations based on the Hasegawa–Mima equation show that for a weak DW turbulence, Φ = ( e φ / T e ) ( L n / ρ s ) ⪝ 1, the collapsing-like features on both ZF and y-averaged enstrophy of DW turbulence decay in time and then re-emerge again at different locations. For the case of a strong DW turbulence, Φ > 1, where nonlinear interactions of DW harmonics dominate, stable spatial structures of ZF and y-averaged enstrophy of DW turbulence emerge.

A method to quantify the energy transfer among turbulent structures using singular value decomposition (SVD) is presented. We apply the method to numerical turbulence data obtained from a global plasma simulation using the Hasegawa–Wakatani fluid model, in which the Kelvin–Helmholtz instability plays a dominant role. Using the SVD method, the electrostatic potential is decomposed into a background potential deformation, a zonal flow, a coherent mode and an intermittent structure. Thus there are four key structures, as distinct from the three found in conventional theory. The kinetic energy of each structure is evaluated, and the limit cycle among them is obtained. In the limit cycle, an abrupt change of the background is found to be synchronised with the period of the zonal flow. The energy transfer function of each turbulence structure, which is defined on the basis of a vorticity equation, is evaluated. This then provides physical understanding of how the limit cycle is sustained by dynamical changes in the energy transfer among structures over the its period. In addition, it is shown that the abrupt deformation of the background is caused by the non-linear self-coupling of the intermittent structure.

This study explores the role of inertial instability in poleward momentum surges and “flare ups” of the subpolar jet near midlatitude cyclones. Two cases are simulated with the University of Wisconsin Nonhydrostatic Modeling System to investigate the mechanisms involved in jet accelerations downstream of quasi-stationary “digging troughs.” Deep convection along the cold front leads to regions of inertial instability in the upper troposphere, which are intimately linked to jet accelerations. Terms in the zonal and meridional wind equations following the motion are evaluated for a selected air parcel within the inertially unstable region. A two-stage synoptic evolution is diagnosed, which is a characteristic signature of inertial instability. First, meridional flow accelerates following the motion, because of the subgeostrophic zonal flow and strong northward pressure gradient force (a statement of inertial instability). Second, supergeostrophic poleward flow leads to zonal acceleration and a jet flare-up. Inertial instability thus effectively displaces a westerly jet maximum poleward relative to inertially stable conditions. The structure of the poleward surge involves a distinctive “head” of high angular momentum, with the region of inertial instability enclosing the jet maximum and a core of strongly negative potential vorticity inside the surge. Departures from angular momentum–conserving profiles during meridional displacement are interpreted in terms of the pressure gradient force and degree of inertial stability. Inertial instability reduces the resulting zonal wind profile relative to angular momentum conservation but provides a significant poleward displacement of the resulting zonal wind maximum.

Meteor radar data collected over Langfang, China (39.4&deg, N, 116.7&deg, E) were used to estimate the momentum flux of short-period (less than 2 h) gravity waves (GWs) in the mesosphere and lower thermosphere (MLT), using the Hocking (2005) analysis technique. Seasonal variations in GW momentum flux exhibited annual oscillation (AO), semiannual oscillation (SAO), and quasi-4-month oscillation. Quantitative estimations of GW forcing toward the mean zonal flow were provided using the determined GW momentum flux. The mean flow acceleration estimated from the divergence of this flux was compared with the observed acceleration of zonal winds displaying SAO and quasi-4-month oscillations. These comparisons were used to analyze the contribution of zonal momentum fluxes of SAO and quasi-4-month oscillations to zonal winds. The estimated acceleration from high-frequency GWs was in the same direction as the observed acceleration of zonal winds for quasi-4-month oscillation winds, with GWs contributing more than 69%. The estimated acceleration due to Coriolis forces to the zonal wind was studied, the findings were opposite to the estimated acceleration of high-frequency GWs for quasi-4-month oscillation winds. The significance of this study lies in estimating and quantifying the contribution of the GW momentum fluxes to zonal winds with quasi-4-month periods over mid-latitude regions for the first time.

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., Comment: 17 pages, selected paper from the 17th Russian Gravitational Conference - International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17), Saint Petersburg, 28 June - 4 July 2020

We examine stability of the polar vortex that initiates planetary-scale westerly (west to east) atmospheric flow that encircles the pole in middle or high latitude of a planet. In our studies, the polar vortex is modeled as an annular flow (zonal flow) extending radially from a rigid inner boundary to a free outer boundary on a E k − plane, which is parallel to the equatorial plane but generally displaced in latitude. The vortex is associated with a particular class of exact solution of a nonlinear two-dimensional free boundary problem on the nonstationary motion of a perfect fluid propagating around a solid circle with a sufficiently large radius with included Coriolis effect. The intensity of the polar vortex is parametrized by means of the “average” (in vertical) zonal flow that can be associated with atmospheric flow patterns that are parallel or nearly parallel to the lines of latitude. Perturbations are allowed in the zonal and nominally vertical (inward–outward) direction. A linear stability analysis purportedly suggests that increasing latitude decreases the maximum strength of the vortex that is permitted for stability. Three essential parameters that control stability of the vortex are identified.

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.

The influence of the recent deep and prolonged solar minimum on the daytime zonal and vertical plasma drift velocities during quiet time is investigated in this work. Analyzing the data obtained from incoherent scatter radar from Jicamarca (11.95° S, 76.87° W) we observe an anomalous behavior of the zonal plasma drift during June 2008 characterized by lower than usual daytime westward drift and its early afternoon reversal to eastward. As a case study the zonal drift observed on 24 June 2008 is modeled using a realistic low-latitude ionosphere simulated by the Sheffield University Plasmasphere-Ionosphere Model-INPE (SUPIM-INPE). The results show that an anomalously low zonal wind was mainly responsible for the observed anomalous behavior in the zonal drift. A comparative study of the vertical plasma drifts obtained from magnetometer data for some periods of maximum (2000–2002) and minimum solar activity (1998, 2008, 2010) phases reveal a considerable decrease on the E-region conductivity and the dynamo electric field during 2008. However, we believe that the contribution of these characteristics to the unusual behavior of the zonal plasma drift is significantly smaller than that arising from the anomalously low zonal wind. The SUPIM-INPE result of the critical frequency of the F layer (foF2) over Jicamarca suggested a lower radiation flux than that predicted by solar irradiance model (SOLAR2000) for June 2008.

The dipole structure of the North Atlantic Oscillation (NAO) is examined in this study by defining the tilt of the NAO dipole centers on synoptic time scales. All the positive NAO phase (NAO+) and negative NAO phase (NAO&minus, ) events are divided into three tilting types according to their definition, namely, northeast&ndash, southwest (NE&ndash, SW), north&ndash, south symmetric (N&ndash, S, not tilted), and northwest&ndash, southeast (NW&ndash, SE) tilting NAO events. Then, the associated surface air temperature (SAT), geopotential height, zonal wind, and SST (surface sea temperature) anomalies of each type are examined. It is found that, for different asymmetric NAO tilt types, the local SATs exhibit significantly different distributions. The zonal wind has a good match with the NAO dipole tilt, which also includes the positive feedback of the NAO circulation. The basic zonal flow that removes the NAO days also exhibits a clear tilt structure that favors the tilt of the NAO dipole. Moreover, it is found that the Atlantic Multidecadal Oscillation (AMO) may be an important factor affecting the tilt of the NAO dipole. The AMO index has a significant 15-year lead for the NAO index and basic zonal flow index, with a high correlation coefficient, which might be seen as a precondition that indicates the tilt of the NAO events, especially on decadal or multidecadal time scales. However, the physical mechanisms and processes are still not fully understood.

The pattern of migrating zonal flow bands associated with the solar cycle, known as the torsional oscillation, has been monitored with continuous global helioseismic observations by the Global Oscillations Network Group, together with those made by the Michelson Doppler Imager onboard the Solar and Heliosepheric Observatory and its successor the Helioseismic and Magnetic Imager onboard the Solar Dynamics Observatory, since 1995, giving us nearly two full solar cycles of observations. We report that the flows now show traces of the mid-latitude acceleration that is expected to become the main equatorward-moving branch of the zonal flow pattern for Cycle 25. Based on the current position of this branch, we speculate that the onset of widespread activity for Cycle 25 is unlikely to be earlier than the middle of 2019., Comment: 8 pages, 5 figures, accepted by ApJL 5 July 2018

An instability involving the resonant interaction of a Rossby wave and a Kelvin wave has been proposed to drive equatorial superrotation in planetary atmospheres with a substantially smaller radius or a smaller rotation rate than Earth, that is, with a large thermal Rossby number. To pursue this idea, this paper investigates the equilibration mechanism of Kelvin–Rossby instability by simulating the unforced initial-value problem in a shallow-water model and in a multilevel primitive equation model. Although the instability produces equatorward momentum fluxes in both models, only the multilevel model is found to superrotate. It is argued that the shortcoming of the shallow-water model is due to its difficulty in representing Kelvin wave breaking and dissipation, which is crucial for accelerating the flow in the tropics. In the absence of dissipation, the zonal momentum fluxed into the tropics is contained in the eddy contribution to the mass-weighted zonal wind rather than the zonal-mean zonal flow itself. In the shallow-water model, the zonal-mean zonal flow is only changed by the eddy potential vorticity flux, which is very small in our flow in the tropics and can only decelerate the flow in the absence of external vorticity stirring., P. Z.-G. acknowledges financial support by Grant CGL2015-72259-EXP by the Ministry of Economy and Competitivity of Spain. This work has been partly done during P. Z.-G.’s visit to Princeton, funded by NSF Grant AGS-1733818.

Long-time evolution of large-scale geophysical flows is considered in a β-plane approximation. Motions in an infinite 2-layer model ocean are treated as a system of weakly nonlinear Rossby waves (weak geostrophic turbulence). The evolution of the energy spectrum of the barotropic and the baroclinic modes is investigated on the basis of numerical experiments with the kinetic equation for baroclinic Rossby waves. The basic features of free (nonforced inviscid) spectral evolution of baroclinic flows are similar to those of the barotropic motions. A portion of the energy is transferred to a sharp spectral peak while the rest of it is isotropically distributed. The peak corresponds to an intensive nearly zonal barotropic flow. Typically, this well-defined barotropic zonal anisotropy inhibits the reinforcement of its baroclinic analogy. For a certain set of initial conditions (in particular, if the barotropic zonal flow is not present initially), a zonal anisotropy of both modes is generated. The interplay between the multimodal nearly zonal flow components leads to the excitation of large-scale (several times exceeding the scale of the initial state), mostly meridional, baroclinic motions at the expense of the barotropic nearly zonal flow. The underlying mechanism is explained on the level of elementary mixed-triad interaction. The whole wave field retains its essentially baroclinic as well as spectrally broad nature. It evidently tends towards a thermodynamically equilibrated final state, consisting of the superposition of a (usually barotropic, but occasionally multimodal) zonal flow and a wave system with a Raleigh-Jeans spectrum. This evolution takes place as a multi-staged process, with fast convergence of the modal spectra to a local equilibrium followed by a more gradual adjustment of the energy balance between the modes.

Source at https://doi.org/10.1088/1741-4326/aad28e. Novel mechanisms for zonal flow (ZF) generation for both large relative density fluctuations and background density gradients are presented. In this non-Oberbeck–Boussinesq (NOB) regime ZFs are driven by the Favre stress, the large fluctuation extension of the Reynolds stress, and by background density gradient and radial particle flux dominated terms. Simulations of a nonlinear full-F gyro-fluid model confirm the predicted mechanism for radial ZF propagation and show the significance of the NOB ZF terms for either large relative density fluctuation levels or steep background density gradients.

Solar torsional oscillations are migrating bands of slower- and faster-than-average rotation, which are strongly related to the Sun's magnetic cycle. We perform a long-term study (16 yr) of hemispherical asymmetry in solar torsional oscillation velocity using helioseismic data for the first time. We study the north-south asymmetry in the velocity using the zonal flow velocities obtained by ring diagram analysis of the Global Oscillation Network Group (GONG) Doppler images. We find significant hemispherical asymmetry in the torsional oscillation velocity and explore its variation with respect to depth, time, and latitude. We also calculate the hemispherical asymmetry in the surface velocity measurements from the Mount Wilson Observatory and the zonal flow velocities obtained from the Helioseismic and Magnetic Imager ring diagram pipeline. These asymmetries are found to be consistent with the asymmetry obtained from GONG observations. We show that the asymmetry in near-surface torsional oscillation velocity is correlated with the asymmetry in magnetic flux and sunspot number at the solar surface, with the velocity asymmetry preceding the flux and sunspot number asymmetries. We speculate that the asymmetry in torsional oscillation velocity may help in predicting the hemispherical asymmetry in sunspot cycles., Comment: Accepted for publication in The Astrophysical Journal

Tropospheric eddy-mean flow interaction is formulated in terms of the vertically integrated budget of finite-amplitude wave activity (FAWA). At each latitude the dynamics is governed by three coupled equations for the interior and surface FAWA and barotropic zonal mean zonal flow. In midlatitude austral summer, the budget reveals a largely adiabatic, antiphase covariation of FAWA and the mean flow. A marked periodicity is found for FAWA around 20–30 days, but not the mean flow, consistent with the recently discovered baroclinic annular mode. The difference in the spectra of FAWA and the mean flow arises from (i) distinct spectra of low-level meridional eddy heat flux and the barotropic eddy momentum flux convergence and (ii) a strong thermal damping of surface wave activity: the latter makes the FAWA respond largely to the low-level meridional eddy heat flux at low frequencies, whereas the zonal mean flow responds to the momentum flux convergence whose spectrum is broader and occupies higher frequencies.

The westward drift component of the secular variation is likely to be a signal of waves riding on a background mean flow. By separating the wave and mean flow contributions, we can infer the strength of the “hidden” azimuthal part of the magnetic field within the core. We explore the origin of the westward drift commonly seen in dynamo simulations and show that it propagates at the speed of the slow magnetic Rossby waves with respect to a mean zonal flow. Our results indicate that such waves could be excited in the Earth's core and that wave propagation may indeed play some role in the longitudinal drift, particularly at higher latitudes where the wave component is relatively strong, the equatorial westward drift being dominated by the mean flow. We discuss a potential inference of the RMS toroidal field strength within the Earth's core from the observed drift rate.

We study the solar-cycle variation of the meridional flow in the near-surface layers of the solar convection zone from the surface to a depth of 16 Mm. We have analyzed Global Oscillation Network Group (GONG) Dopplergrams with a ring-diagram analysis covering about 13 years (July 2001 – October 2014), from the maximum of Cycle 23 through the rising phase of Cycle 24, and Helioseismic and Magnetic Imager (HMI) Dopplergrams covering more than four years (May 2010 – January 2015). GONG and HMI lead to similar meridional flows during common epochs and latitudes. The meridional flow averaged over a Carrington rotation is poleward up to about $70^{\circ}$ in both hemispheres at all depths after correcting for systematic effects. The flow amplitude peaks at about $40^{\circ}$ latitude with an amplitude of about 16 to $20~\mbox{m}\,\mbox{s}^{-1}$ depending on depth. The meridional flow varies with the solar cycle; the flow amplitudes are larger during cycle minimum than during maximum at low- and mid-latitudes. The flows are mainly faster or more-poleward-than-average on the equatorward side of the mean latitude of activity and slower or less-poleward-than-average on its poleward side. The residual meridional flow converges near the mean latitude of activity. A comparison with the corresponding zonal flow derived from GONG and HMI data shows that the bands of more-poleward-than-average meridional flow coincide with the bands of faster-than-average zonal flow and that the bands of less-poleward-than-average meridional flow coincide with the bands of slower-than-average zonal flow. This implies that the residual flows are cyclonic. The bands of fast meridional flow appear at mid-latitudes about three years before magnetic activity of Cycle 24 is present in synoptic maps.

International audience; We review some recent results that have been obtained in the investigation of zonal flow emergence, by means of a gyrokinetic trapped ion model, in the regime of ion temperature gradient instabilities for tokamak plasmas. We show that an analogous formulation of the zonal flow dynamics in terms of the Reynolds tensor applies in the fluid and kinetic regimes, where polarization effects play a major role. The kinetic regime leads to the emergence of a resonant mode at a frequency close to the drift frequency. With the objective of modeling both separate fluid and kinetic regimes of zonal flows, we used in this paper a methodology for deriving both Charney–Hasegawa–Mima (CHM) and Hasegawa–Wakatani models. This methodology is based on the trapped ion model and is analogous to the hierarchy leading from the Vlasov equation to the macroscopic fluid equations. The nature of zonal flows in the hierarchy of the Mima, Hasegawa and Wakatani models is investigated and discussed through comparisons with global kinetic simulations. Applications to the CHM equation are discussed, which applies to a broad variety of hydrodynamical systems, ranging from large-scale processes met in magnetically confined plasma to the so-called zonostrophy turbulence emerging in the case of small-scale forced, two-dimensional barotropic turbulence (Sukoriansky et al. Phys. Rev. Letters, 101, 178501, 2008)