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DOE OSTI2026

Quantitative analysis of zonal flow influence on turbulent plasmas driven by trapped electrons

The role of zonal flow (ZF) in the turbulence saturation of trapped electron modes (TEM) in magnetically confined plasmas is revisited. Here, in this study, we examine ZF excitation and saturation mechanisms in TEM turbulence using detailed free-energy transfer diagnostics from nonlinear gyrokinetic simulations. When the ion channel becomes subdominant, electrons shift to transferring energy to the zonal component, which results in zonal flows always playing a significant though subdominant role, in the case of the temperature gradient driven TEM. The velocity-space structure of energy transfer reveals that trapped electrons directly couple to ZF. Regarding the saturation physics, the zonal flow advection, drift-wave–drift-wave interactions, and stable modes at the pump waves are compared. When ZF saturation is weak, drift-wave–drift-wave interactions play a larger role in maintaining turbulence saturation. The findings elucidate the roles of nonzonal to zonal flow coupling, stable modes, and nonzonal wave-wave interactions, and provide a basis for improving reduced models of turbulent transport.

Song, Jiheon [Hanyang University, Seoul (Korea, Re↗

DOE OSTI2021

Transmission Capacity Allocation in Zonal Electricity Markets

In this work, we propose a novel framework for modeling zonal electricity markets, based on projecting the constraints of the nodal network onto the space of the zonal aggregation of the network. The framework avoids circular definitions and discretionary parameters, which are recurrent in the implementation and study of zonal markets. Using this framework, we model and analyze two zonal market designs currently present in Europe: flow-based market coupling (FBMC) and available-transfer-capacity market coupling (ATCMC). We develop cutting-plane algorithms for simulating FBMC and ATCMC while accounting for the robustness of imports/exports to single element failures, and we conduct numerical simulations of FBMC and ATCMC on a realistic instance of the Central Western European system under the equivalent of 100 years of operating conditions. We find that FBMC and ATCMC are unable to anticipate the congestion of branches interconnecting zones and branches within zones and that both zonal designs achieve similar overall cost efficiencies (0.01% difference), whereas a nodal market design largely outperforms both of them (5.09% better than FBMC). These findings raise the question of whether it is worth it for more European countries to switch from ATCMC to FBMC, instead of advancing directly toward a nodal market design.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Zonal Flow and Self-regulating Mechanism in a Hydrodynamic Disk

This study addresses key aspects of momentum transport in hydrodynamic disks, which is critical for understanding zonal flow generation and turbulence in compressible hydrodynamic disks. We find that nonlinear momentum/density transport leads to the formation of zonal flows from the Rossby wave instability in disks. We analytically derive the generation and location of zonal flows and describe a modified Taylor identity applicable to compressible disk flows. We further present a self-regulation model, revealing a dynamic interplay between zonal flow and fluctuations driven by Rossby wave instability that regulates the nonlinear saturation state. This theoretical framework contributes insights into the dynamics of disks such as protoplanetary disks, shedding light on the intricate processes governing momentum/density transport and the emergence of zonal flows in the saturation of protoplanetary disks.

Astrophysical fluid dynamics↗

NASA NTRS1981

Computation of averaged monthly zonal albedo utilizing the solar zenith angle, properties of clear and cloudy atmospheres

The zonal temporal averages of albedos at the top of the atmosphere were considered as a function of the length of the day. The length of the day were used to determine the average daily values of mu sub 0(=Cos of the solar zenith angle, theta sub 0). Polynominal fits of the slope and intercept functions of A sub s (cloud-free albedo) and A sub c(cloud albedo) as function of Cos theta sub 0 were obtained by using the sample values of albedo corresponding to solar zenith angles from 0 to 90 deg with interval of 5 deg. The daily zonal values of mu sub 0 and the surface albedos were used to compute the daily zonal values of albedos at the top of the clear and cloudy atmosphere. The monthly zonal cloud fractions were used to compute planetary albedo A at the top of the atmosphere. The global values of monthly albedos A sub s, A sub c and A were computed by using the weighting function defined as the difference of the sins of zonal values of latitudes. The computer program implementation is also described.

Dhuria, H.↗

NASA NTRS1982

The latitude dependence of the variance of zonally averaged quantities

Geometric characteristics of the spherical earth are shown to be responsible for the increase of variance with latitude of zonally averaged meteorological statistics. An analytic model is constructed to display the effect of a spherical geometry on zonal averages, employing a sphere labeled with radial unit vectors in a real, stochastic field expanded in complex spherical harmonics. The variance of a zonally averaged field is found to be expressible in terms of the spectrum of the vector field of the spherical harmonics. A maximum variance is then located at the poles, and the ratio of the variance to the zonally averaged grid-point variance, weighted by the cosine of the latitude, yields the zonal correlation typical of the latitude. An example is provided for the 500 mb level in the Northern Hemisphere compared to 15 years of data. Variance is determined to increase north of 60 deg latitude.

North, G. R.↗

NASA NTRS1985

An implicit, conservative, zonal-boundary scheme for Euler equation calculations

A zonal, or patched, grid approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. A conservative, zonal boundary condition that could be used with explicit schemes was extended so that it can be used with existing second order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, M. M.↗

NASA NTRS1985

An implicit, conservative, zonal-boundary scheme for Euler equation calculations

A 'zonal', or 'patched-grid', approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order-accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, M. M.↗

NASA NTRS1984

The generation of mesospheric planetary waves by zonally asymmetric gravity wave breaking

A semispectral numerical model is used to study the influence of a longitudinally varying gravity wave source on the general circulation of the winter mesosphere. The gravity wave source consists of stationary (topographic) waves with a longitudinally varying amplitude distribution that is approximated by the first two terms in a zonal harmonic expansion (i.e., the zonal mean plus planetary wavenumber 1). The computed zonal mean circulation in the mesosphere is nearly the same as that computed for a zonally symmetric gravity wave source of equal amplitude. However, the asymmetric source excites a strong stationary wavenumber 1 disturbance near the level of gravity wave breaking (equal to about 71 km). This disturbance has a zonal wind maximum about 1/4-cycle upstream from the gravity wave drag maximum. It is concluded that vertically propagating gravity waves produced in the troposphere are a possible source for mesospheric planetary waves.

Holton, J. R.↗

NASA NTRS1987

Rossby waves and two-dimensional turbulence in a large-scale zonal jet

Homogeneous barotropic beta-plane turbulence is investigated, taking into account the effects of spatial inhomogeneity in the form of a zonal shear flows. Attention is given to the case of zonal flows that are barotropically stable and of larger scale than the resulting transient eddy field. Numerical simulations reveal that large-scale zonal flows alter the picture of classical beta-plane turbulence. It is found that the disturbance field penetrates to the largest scales of motion, that the larger disturbance scales show a tendency to meridional rather than zonal anisotropy, and that the initial spectral transfer rate away from an isotropic intermediate-scale source is enhanced by the shear-induced transfer associated with straining by the zonal flow.

Shepherd, Theodor G.↗

NASA NTRS1988

Zonally symmetric response to atmospheric tidal forcing in the dusty Martian atmosphere

The paper presents a steady state, zonally symmetric response of an atmospheric circulation to the combined effects of the very large zonal-mean diabatic heating and thermotidal forcing thought to exist in the dusty Martian atmosphere during one of its episodic global dust storms. The zonal-mean components of the tidal flux-convergences of momentum and heat are computed using an existing classical atmospheric tidal model constrained by the surface pressure observations at the two Viking Lander sites on Mars. A nearly inviscid two-dimensional model is used to compute the zonally symmetric response to the computed tidal flux-convergences and to the zonal-mean heating of the airborne dust. The results are compared with data from the Viking missions.

Zurek, Richard W.↗

NASA NTRS1993

Zonal mean winds in the equatorial mesosphere and lower thermosphere observed by the High Resolution Doppler Imager

This paper presents analyses of mesospheric and lower thermospheric zonal mean winds observed by the High Resolution Doppler Imager (HRDI) on the Upper Atmosphere Research Satellite (UARS). Monthly averages of the equatorial zonal mean zonal winds are presented for January 1992 through June 1993. Equatorial zonal winds in the 70-90 km region are dominated by a semiannual oscillation (SAO), ranging from 30 m/s (westerly) to -100 m/s (easterly). At high latitudes the zonal wind variations are predominantly annual. Above 90 km, the low-latitude flow is easterly at all times, punctuated by a small semiannual variation. This behavior may be related to the deposition of momentum by the diurnal tides.

Lieberman, R. S.↗

NASA NTRS1986

An Implicit, Conservative, Zonal-Boundary Scheme for Euler Equation Calculations

A "zonal," or "patched-grid," approach is one in which the flow region of interest is divided into subregions which are then discretized independently, using existing grid generators. The equations of motion are integrated in each subregion in conjunction with zonal-boundary schemes which allow proper information transfer across interfaces that separate subregions. The zonal approach greatly simplifies the treatment of complex geometries and also the addition of grid points to selected regions of the flow. In this study a conservative, zonal-boundary condition that could be used with explicit schemes has been extended so that it can be used with existing second-order accurate implicit integration schemes such as the Beam-Warming and Osher schemes. In the test case considered, the implicit schemes increased the rate of convergence considerably (by a factor of about 30 over that of the explicit scheme). Results demonstrating the time-accuracy of the zonal scheme and the feasibility of performing calculations on zones that move relative to each other are also presented.

Rai, Man Mohan↗

DOE OSTI2021

Global gyrokinetic simulation with kinetic electron for collisionless damping of zonal flow in stellarators

Global gyrokinetic simulations with kinetic electrons for collisionless damping of zonal flows in LHD and W7-X stellarators show that the helical components of the equilibrium magnetic field responsible for helically trapped particles have significant impacts on zonal flow. Kinetic electrons reduce zonal flow residue and increase the frequency of low frequency oscillation (LFO). Here, the LFO is induced by dominant helical harmonics of magnetic field strength. Furthermore, linear toroidal coupling of multiple toroidal n-harmonics barely affects the zonal flows, but can generate long wavelength toroidal harmonics with the same toroidal number as the helical magnetic field.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2025

Alfvén eigenmode-driven zonal modes saturate and heat thermal ions by cross-scale interactions

In scenarios where a sustained energetic particle source strongly drives toroidal Alfvén eigenmodes (TAE), and phase-space transport is insufficient to saturate TAE, this novel theory of TAE-zonal mode (ZM)-turbulence—self-regulated by cross-scale interactions (including collisionless ZF damping) – merits consideration. Zonal modes are driven by Reynolds and Maxwell stresses, without the onset of modulational instability. TAE evolution in the presence of ZMs conserves energy and closes the system feedback loop. The saturated zonal shears can be sufficient to suppress ambient drift-ion temperature gradient (ITG) turbulence, achieving an enhanced core confinement regime. The saturated state is regulated by linear and turbulent zonal flow drag. This regulation leads to bursty TAE spectral oscillations, which overshoot while approaching saturation. Heating by both collisional and collisionless ZM damping deposits alpha particle energy into the thermal plasma, achieving effective alpha channeling. This theory offers a mechanism for EP-induced transport barrier formation, and predicts a novel thermal ion heating mechanism.

ITB↗

DOE OSTI2023

The Zonal Patterns in Late Quaternary Tropical South American Precipitation

Speleothem oxygen isotope records (δ 18 O) of tropical South American rainfall in the late Quaternary show a zonal “South American Precipitation Dipole” (SAPD). The dipole is characterized by opposing east-west precipitation anomalies compared to the present—wetter in the east and drier in the west at the mid-Holocene (~7 ka), and drier in the east and wetter in the west at the Last Glacial Maximum (~21 ka). However, the SAPD remains enigmatic because it is expressed differently in western versus eastern δ18O records and isotope-enabled climate model simulations usually misrepresent the magnitude and/or spatial pattern of δ 18 O change. Here, we address the SAPD enigma in two parts. First, we re-interpret the δ 18 O data to account for upwind rainout effects that are known to be pervasive in tropical South America, but are not always considered in Quaternary paleoclimate studies. Our revised interpretation reconciles the δ 18 O data with cave infiltration and other proxy records, and indicates that the centroid of tropical South American rainfall has migrated zonally over time. Second, using an energy balance model of tropical atmospheric circulation, we hypothesize that zonal migration of the precipitation centroid can be explained by regional energy budget shifts, such as changing Saharan albedo associated with the African Humid Period, that have not been modeled in previous SAPD studies. This hypothesis of a migrating precipitation centroid presents a new framework for interpreting δ18O records from tropical South America and may help explain the zonal rainfall anomalies that predate the late Quaternary.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Wave-kinetic approach to zonal-flow dynamics: Recent advances

The basic physics of drift-wave turbulence and zonal flows has long been studied within the framework of the wave-kinetic theory. Recently, this framework has been reexamined from first principles, which has led to more accurate yet still tractable “improved” wave-kinetic equations. In particular, these equations reveal an important effect of the zonal-flow “curvature” (the second radial derivative of the flow velocity) on the dynamics and stability of drift waves and zonal flows. Here, we overview these recent findings and present a consolidated high-level picture of (mostly quasilinear) zonal-flow physics within reduced models of drift-wave turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Solitary zonal structures in subcritical drift waves: a minimum model

Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we show that similar structures can be obtained within a reduced model, which complements the modified Hasegawa–Mima equation with a generic primary instability and a background shear flow. We also find that these structures can be qualitatively reproduced in the modified Hasegawa–Wakatani equation, which subsumes the reduced model as a limit. In particular, we illustrate that in both cases, the solitary zonal structures approximately satisfy the same 'equation of state', which is a local relation connecting the DW envelope with the zonal-flow velocity. Due to this generality, our reduced model can be considered as a minimum model for solitary zonal structures in subcritical DWs.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Zonal flow screening in negative triangularity tokamaks

Here, 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.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗