Dataset for "Theory of zonal flow generation and propagation in toroidal geometry"
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A model of mean zonal flows in the major planets
The linear theory of deep zonal flows developed by Busse (1976) for the origins of deep motions of the atmospheres of Jupiter and Saturn is extended into the nonlinear regime. Relationships for the relative magnitudes of convective heat and momentum transports are formulated. A perturbation approach is taken to the problem, with the amplitude of the convection serving as the small parameter, and the basic equations being expanded in terms of the Prandtl number. The Boussinesq approximation is employed, together with an assumption of a low Rossby number for the Jovian and Saturn atmospheres. Differences in the amplitude of the Jovian equatorial jet relative to that of Saturn are explored in terms of a low equatorial convective heat flux on Jupiter.
Busse, F. H.↗
Influence of zonal flow and density on resistive drift wave turbulent transport
The generations of zonal flow (ZF) and density (ZD) and their feedback on the resistive drift wave turbulent transport are investigated within the modified Hasegawa-Wakatani model. With proper normalization, the system is only controlled by an effective adiabatic parameter, a, where the ZF dominates the collisional drift wave (DW) turbulence in the adiabatic limit a > 1. By conducting direct numerical simulations, we found that the ZF can significantly reduce the transport by trapping the DWs in the vicinities of its extrema for a > 1, whereas the ZD itself has little impact on the turbulence but can only assist ZF to further decrease the transport by flattening the local plasma density gradient.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Barotropic instability of weakly non-parallel zonal flows
Integrations of the linear stability problem, in the present numerical investigation of weakly nonparallel zonal flows barotropic instability having localized intense shear regions, reveal the existence of unstable localized wave packets. The spatial structure and eigenfrequencies of these packets depend on two parameters measuring the degree of supercriticality and the zonal length scale of the shear region. It is found that instability structure is defined by conditions ensuring the decay of the wave packet at infinity, and the transition from long to short waves across a turning point region that is controlled by nonparallel effects.
Merkine, L.-O.↗
Stability of zonal flows on Jupiter
Gierasch et al. (1979) have shown that the question of the stability of zonal flows on Jupiter is influenced strongly by the lower boundary condition. In the case of Jupiter, the troposphere rests above a deep layer of fluid which is probably extremely close to adiabatic. The present study extends the earlier investigations to a wider range of conditions, taking into account the nongeostrophic limit and the presence of horizontal shear. The major difference between the behavior of the model derived in the study and the behavior of a model with a rigid lower boundary, corresponding to the terrestrial conditions, is that baroclinic instability by the Eady mechanism is suppressed. The influence of beta (Charney-type instability) operates only at the top of the troposphere, not at its base. The suppression of the Eady modes seems to apply all the way down to the nongeostrophic limit where the Rossby number is order unity.
Conrath, B. J.↗
Drift waves enstrophy, zonal flow, and nonlinear evolution of the modulational instability
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.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Theory of zonal flow growth and propagation in toroidal geometry
The toroidal geometry of tokamaks and stellarators is known to play a crucial role in the linear physics of zonal flows (ZFs), leading to e.g. the Rosenbluth–Hinton residual and geodesic acoustic modes. However, descriptions of the nonlinear ZF growth from a turbulent background typically resort to simplified models of the geometry. We present a generalised theory of the secondary instability to model the ZF growth from turbulent fluctuations in toroidal geometry, demonstrating that the radial magnetic drift substantially affects the nonlinear ZF dynamics. In particular, the toroidicity gives rise to a new branch of propagating ZFs, the toroidal secondary mode, which is nonlinearly supported by the turbulence. We present a theory of this mode and compare the theory against gyrokinetic simulations of the secondary mode. The connection with other secondary modes—the ion-temperature-gradient and Rogers–Dorland–Kotschenreuther secondary modes—is also examined.
Nies, Richard [Princeton Univ., NJ (United States)↗
On the Regionality of Moist Kelvin Waves and the MJO: The Critical Role of the Background Zonal Flow
Abstract A global model with superparameterized physics is used to shed light on the observed regionality of convectively coupled Kelvin waves and the Madden‐Julian Oscillation (MJO). A series of aquaplanet simulations over zonally uniform sea‐surface temperatures is performed, in which the axisymmetric structure of the background zonal flow is altered through nudging, while maintaining a quasi‐fixed rainfall climatology. Results show that nudging at the equator to match profiles typical of the Indo‐Pacific or eastern Pacific sectors yields eastward‐moving tropical rain spectra typical of those sectors. Two different mechanistic pathways are identified as being responsible for this mean‐flow dependence, in addition to Doppler shifting effects. The first is through shifts of the Rossby wave critical line in the subtropical upper troposphere that affect the lateral forcing of Kelvin‐mode circulations at the equator by eastward and equatorward‐propagating eddies impinging on the tropics from higher latitudes. The second is through changes in the strength of the mean cyclonic shear in the lower tropical troposphere that affect the degree to which intraseasonal fluctuations in Kelvin‐mode zonal winds modulate the activity of higher‐frequency equatorial Rossby‐type eddies. In cases where the mean low‐level cyclonic shear is enhanced, the strength of this modulation, referred to as “shear‐induced eddy modulation” or SIEM, is also seen to be enhanced, such that MJO‐like modes of variability are rendered either unstable or near neutral, depending on the strength of the shear.
Tulich, S. N.↗
Jupiter - New estimates of the mean zonal flow at the cloud level
In order to reexamine the magnitude differences of the Jovian atmosphere's jets, as determined by Voyager 1 and 2 images, a novel approach is used to ascertain the zonal mean east-west component of motion. This technique is based on digital pattern matching, and is applied on pairs of mapped images to yield a profile of the mean zonal component that reproduces the exact locations of the easterly and westerly jets between + and - 60 deg latitude. Results have been obtained for all of the Voyager 1 and 2 cylindrical mosaics; the correlation coefficient between Voyagers 1 and 2 in mean zonal flow between + and - 60 deg latitude, determined from violet filter mosaics, is 0.998.
Limaye, S. S.↗
Jupiter: New estimates of mean zonal flow at the cloud level
In order to reexamine the magnitude differences of the Jovian atmosphere's jets, as determined by Voyager 1 and 2 images, a novel approach is used to ascertain the zonal mean east-west component of motion. This technique is based on digital pattern matching, and is applied on pairs of mapped images to yield a profile of the mean zonal component that reproduces the exact locations of the easterly and westerly jets between + and 60 deg latitude. Results were obtained for all of the Voyager 1 and 2 cylindrical mosaics; the correlation coefficient between Voyagers 1 and 2 in mean zonal flow between + and - 60 deg latitude, determined from violet filter mosaics, is 0.998.
Limaye, Sanjay S.↗
Zonal flow excitation in electron-scale tokamak turbulence
Abstract The derivation of an intermediate-scale gyrokinetic-electron theory in nonuniform tokamak plasmas (Chen et al 2021 Nucl. Fusion 61 066017 ) has shown that a Navier–Stokes type nonlinearity couples electron-temperature-gradient (ETG) modes and zonal flow (ZF) modes with wavelengths much shorter than the ion gyroradius but much longer than the electron gyroradius. This intermediate-scale ETG-ZF coupling is typically stronger than the Hasegawa–Mima type nonlinearity characteristic of the fluid approximation and is predicted to lead to relevant ZF generation and ETG mode regulation. Electron-scale, continuum, gyrokinetic simulation results are presented here which include both single-mode ETG and full-spectrum ETG turbulence. The ZF generation due to single ETG modes is investigated and the single-mode intermediate-scale results are found to be in agreement with theory. The full-spectrum results are then presented and explained qualitatively in terms of the single-mode results. It is found that the ETG-driven ZFs regulate intermediate-scale electron heat flux transport to levels in the predicted range.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Boundary zonal flows in rapidly rotating turbulent thermal convection
Recently, in Zhang et al. ( Phys. Rev. Lett. , vol. 124, 2020, 084505), it was found that, in rapidly rotating turbulent Rayleigh–Bénard convection in slender cylindrical containers (with diameter-to-height aspect ratio $\varGamma =1/2$ ) filled with a small-Prandtl-number fluid ( ${Pr}\approx 0.8$ ), the large-scale circulation is suppressed and a boundary zonal flow (BZF) develops near the sidewall, characterized by a bimodal probability density function of the temperature, cyclonic fluid motion and anticyclonic drift of the flow pattern (with respect to the rotating frame). This BZF carries a disproportionate amount ( ${>}60\,\%$ ) of the total heat transport for ${Pr} < 1$ , but decreases rather abruptly for larger ${Pr}$ to approximately $35\,\%$ . In this work, we show that the BZF is robust and appears in rapidly rotating turbulent Rayleigh–Bénard convection in containers of different $\varGamma$ and over a broad range of ${Pr}$ and ${Ra}$ . Furthermore, tirect numerical simulations for Prandtl number $0.1 \leq {\textit {Pr}} \leq 12.3$ , Rayleigh number $10^7 \leq {Ra} \leq 5\times 10^{9}$ , inverse Ekman number $10^{5} \leq 1/{\textit {Ek}} \leq 10^{7}$ and $\varGamma = 1/3$ , 1/2, 3/4, 1 and 2 show that the BZF width $\delta _0$ scales with the Rayleigh number ${Ra}$ and Ekman number ${\textit {Ek}}$ as $\delta _0/H \sim \varGamma ^{0} Pr^{\{-1/4, 0\}} {Ra}^{1/4} {\textit {Ek}}^{2/3}$ ( $\{{\textit {Pr}}<1, {\textit {Pr}}>1\}$ ) and with the drift frequency scales as $\omega /\varOmega \sim \varGamma ^{0} Pr^{-4/3} {Ra}\,{\textit {Ek}}^{5/3}$ , where $H$ is the cell height and $\varOmega$ the angular rotation rate. The mode number of the BZF is 1 for $\varGamma \lesssim 1$ and $2 \varGamma$ for $\varGamma = \{1,2\}$ independent of ${Ra}$ and ${Pr}$ . The BZF is quite reminiscent of wall mode states in rotating convection.
42 ENGINEERING↗
Saturn meteorology - A diagnostic assessment of thin-layer configurations for the zonal flow
Voyager imaging, infrared, and radio observations for Saturn have been recently interpreted by Smith et al. (1982) as an indication that the jet streams observed at the cloud tops extend to depths greater than the 10,000-bar level. This analysis assumes a maximum latitudinal temperature contrast of a few percent, a mean atmospheric rotation rate at depth given by Saturn's ratio period, and no variation with latitude of the bottom pressure level for the zonal flow system. These assumptions are not, however, firmly constrained by observation. The diagnostic analysis of plausible alternative configurations for Saturn's atmospheric structure demonstrates that a thin weather layer system (confined at mid to high latitudes to levels above 200 bar) cannot be excluded by any of the available observations. A quantitative estimate of the effects of moisture condensation (including the differentiation of mean molecular weight) suggests that these might provide the buoyancy contrasts necessary to support a thin-layer flow provided that Saturn's outer envelope is enriched approximately 10 times in water abundance relative to a solar composition atmosphere and strongly differentiated with latitude at the condensation level.
Allison, M.↗
Hydromagnetic constraints on deep zonal flow in the giant planets
A simple model of the equatorial zonal jet in the giant planets is studied in which the flow is assumed uniform on cylinders concentric with the spin axis, and viscous and magnetic torques on each cylinder are balanced. This 'Taylor constraint' is solved simultaneously with the dynamo equation to obtain the velocity and magnetic field in the equatorial plane. The model is used to reproduce the widely differing jet widths of Jupiter and Saturn eddy viscosity of 2500 sq cm/s. For Saturn, the model has a large magnetic Reynolds number where the Chandrasekhar number Q = 1, and hence exhibits substantial axisymmetrization of the field in the equatorial plane.
Kirk, R. L.↗
Collisionless zonal-flow dynamics in quasisymmetric stellarators
The linear collisionless plasma response to a zonal-density perturbation in quasisymmetric stellarators is studied, including the geodesic-acoustic-mode oscillations and the Rosenbluth–Hinton residual flow. While the geodesic-acoustic-mode oscillations in quasiaxisymmetric configurations are similar to tokamaks, they become non-existent in quasi-helically symmetric configurations when the effective safety factor in helical-angle coordinates is small. Compared with concentric-circular tokamaks, the Rosenbluth–Hinton residual is also found to be multiplied by a geometric factor $\mathcal {C}$ that arises from the flux-surface-averaged classical polarization. Using the near-axis-expansion framework, we derive an analytic expression for $\mathcal {C}$ , which varies significantly among different configurations. These analytic results are compared with numerical simulation results from the global gyrokinetic particle-in-cell code GTC, and good agreement with the theoretical Rosenbluth–Hinton residual level is achieved when the quasisymmetry error is small enough.
Zhu, Hongxuan (ORCID:0000000198446972)↗
The behavior of planetary wave 2 in preconditioned zonal flows
The response of linear planetary wave 2 to changes in the isentropic zonally symmetric distribution of potential vorticity (PV) is investigated numerically. Wave 2 is sensitive to the width and position of a region where the meridional derivative of PV is weak, denoted the 'surf zone', in the middle stratosphere. A narrow surf zone leads to an amplification of wave 2, and confines some of its Eliassen-Palm wave activity in high latitudes. For wider surf zones the wave activity is concentrated near the associated critical surface, and the amplitude of the wave decreases. Large changes in the wave amplitude and in the distribution of its activity are associated with the subtle changes in the zonal winds produced by modest modifications in the distribution of PV. Basic states that include regions of reversed meridional gradients of PV lead to wave overreflection and strong poleward focusing of wave activity. The amplitude of wave 2 is enhanced in the presence of negative gradients, with large responses occurring for eastward traveling waves.
Robinson, Walter A.↗
A zonal flow analysis method for two-dimensional airfoils
A closed-loop, overlapped, velocity-coupling procedure has been utilized to combine a two-dimensional potential flow panel code and a Navier-Stokes code. The fully coupled, two-zone code has been used to compute the flow past a NACA 0012 airfoil. For this case, the zonal method has shown that the grid domain size can be reduced to 0.14 chord lengths with less than 1 percent loss in accuracy. Further, the required computation time is reduced by a factor of approximately four.
Summa, J. Michael↗
Barotropic stability of westward-moving waves in realistic stratospheric zonal flows
A linearized barotropic model on a sphere is used to study the stability of a basic state composed of a westward-moving wave and a zonal mean jet. It is found that the inclusion of a very weak jet in the basic state dramatically alters the stability of the flow. The alteration of stability characteristics for realistic summer and winter jets is discussed.
Manney, Gloria L.↗