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All sourcesNASA NTRSDOE OSTI
NASA NTRS2008

Field Observations of Soil Moisture Variability across Scales

In this study, over 36,000 ground-based soil moisture measurements collected during the SGP97, SGP99, SMEX02, and SMEX03 field campaigns were analyzed to characterize the behavior of soil moisture variability across scales. The field campaigns were conducted in Oklahoma and Iowa in the central USA. The Oklahoma study region is sub-humid with moderately rolling topography, while the Iowa study region is humid with low-relief topography. The relationship of soil moisture standard deviation, skewness and the coefficient of variation versus mean moisture content was explored at six distinct extent scales, ranging from 2.5 m to 50 km. Results showed that variability generally increases with extent scale. The standard deviation increased from 0.036 cm3/cm3 at the 2.5-m scale to 0.071 cm3/cm3 at the 50-km scale. The log standard deviation of soil moisture increased linearly with the log extent scale, from 16 m to 1.6 km, indicative of fractal scaling. The soil moisture standard deviation versus mean moisture content exhibited a convex upward relationship at the 800-m and 50-km scales, with maximum values at mean moisture contents of roughly 0.17 cm3/cm3 and 0.19 cm3/cm3, respectively. An empirical model derived from the observed behavior of soil moisture variability was used to estimate uncertainty in the mean moisture content for a fixed number of samples at the 800-m and 50-km scales, as well as the number of ground-truth samples needed to achieve 0.05 cm3/cm3 and 0.03 cm3/cm3 accuracies. The empirical relationships can also be used to parameterize surface soil moisture variations in land surface and hydrological models across a range of scales. To our knowledge, this is the first study to document the behavior of soil moisture variability over this range of extent scales using ground-based measurements. Our results will contribute not only to efficient and reliable satellite validation, but also to better utilization of remotely sensed soil moisture products for enhanced modeling and prediction.

Famiglietti, James S.↗
NASA NTRS2015

Estimation of Crop Gross Primary Production (GPP): Do Scaled (MODIS) Vegetation Indices Improve Performance? - 2

Satellite remote sensing estimates of Gross Primary Production (GPP) have routinely been made using spectral Vegetation Indices (VIs) over the past two decades. The Normalized Difference Vegetation Index (NDVI), the Enhanced Vegetation Index (EVI), the green band Wide Dynamic Range Vegetation Index (WDRVIgreen), and the green band Chlorophyll Index (CIgreen) have been employed to estimate GPP under the assumption that GPP is proportional to the product of VI and photosynthetically active radiation (PAR) (where VI is one of four VIs: NDVI, EVI, WDRVIgreen, or CIgreen). However, the empirical regressions between VI*PAR and GPP measured locally at flux towers do not pass through the origin (i.e., the zero X-Y value for regressions). Therefore they are somewhat difficult to interpret and apply. This study investigates (1) what are the scaling factors and offsets (i.e., regression slopes and intercepts) between the fraction of PAR absorbed by chlorophyll of a canopy (fAPARchl) and the VIs, and (2) whether the scaled VIs developed in (1) can eliminate the deficiency and improve the accuracy of GPP estimates. Three AmeriFlux maize and soybean fields were selected for this study, two of which are irrigated and one is rainfed. The four VIs and fAPARchl of the fields were computed with the MODerate resolution Imaging Spectroradiometer (MODIS) satellite images. The GPP estimation performance for the scaled VIs was compared to results obtained with the original VIs and evaluated with standard statistics: the coefficient of determination (R2), the root mean square error (RMSE), and the coefficient of variation (CV). Overall, the scaled EVI obtained the best performance. The performance of the scaled NDVI, EVI and WDRVIgreen was improved across sites, crop types and soil/background wetness conditions. The scaled CIgreen did not improve results, compared to the original CIgreen. The scaled green band indices (WDRVIgreen, CIgreen) did not exhibit superior performance to either the scaled EVI or NDVI in estimating crop daily GPP at these agricultural fields. The scaled VIs are more physiologically meaningful than original un-scaled VIs, but scaling factors and offsets may vary across crop types and surface conditions.

Vegetation Index↗
DOE OSTI2024

Transport from electron-scale turbulence in toroidal magnetic confinement devices

Plasma transport driven by turbulence ultimately determines the energy confinement performance of controlled fusion devices regardless of their confinement schemes and configurations. A large variety of plasma instabilities have been proposed for driving turbulence responsible for anomalous plasma transport beyond classical/neoclassical transport due to collisions. Although ion-scale turbulence usually dominates due to its large eddy size and saturation level, electron-scale turbulence has been recognized to be important in regions where ion-scale turbulence is suppressed (e.g., in internal transport barrier and in spherical tokamak H-mode plasmas) or is close to marginality. Electron-scale turbulence has been shown to nonlinearly interact with ion-scale turbulence, which modifies the dynamics of both and affects the resulting plasma transport, particularly when ion-scale instability is weakly driven. In this review paper, we focus on electron-scale turbulence that is believed to operate in magnetically confinement fusion devices and aim to provide a review of theoretical, numerical, and experimental developments in understanding electron-scale turbulence and its role in driving anomalous plasma turbulence. In particular, we focus on the electrostatic electron temperature gradient (ETG) mode which is the most widely recognized plasma instability underlying electron-scale turbulence observed in magnetically confined plasmas. Finally, we note that there are other less studied instabilities that might be responsible for observed electron-scale turbulence, most notably ubiquitous mode, and short-wavelength ion temperature gradient (SWITG) mode, which will be briefly touched on in this review.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Comparative study with two reduced test facilities for air-cooled RCCS scaling law

Korea Atomic Energy Research Institute (KAERI) and Argonne National Laboratory (ANL) conducted steady-state tests at constant heat flux conditions to investigate the scale effect on heat removal behavior of the air-cooled Reactor Cavity Cooling System (RCCS). Two differently scaled-down test facilities were used in this study, KAERI’s ¼ scale with 4.0-m cavity height, and ANL’s ½ scale with 6.8-m cavity height. Two scaling laws were proposed to simulate the radiation across the cavity and the buoyancy-driven duct flow in the riser, respectively. The test matrix for KAERI and ANL test facilities focused on the scaling effect of the heated riser length with constant heat flux at the PMR200 RCCS design. The test results showed that mixed convection in the riser duct is an important factor for accurately extrapolating the thermo-fluid behavior in the prototype from the test results in the scale-down facilities. The system analysis code, GAMMA+, with improved heat transfer models predicted fairly well the air-cooled RCCS test data from two facilities. GAMMA+ analysis results showed that the predicted radiation fractions on the heated plate in the scale-down test conditions were larger than those on the reactor vessel in the prototype. The scaling law for air-cooled RCCS was improved by considering the mixed convection in the riser duct and the same radiation fraction on the heated plate. The mixed convection effect was calculated by the height ratio. The same radiation fraction provided a conservative extrapolation from the scale-down test results.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2026

Enabling microbial electrolysis cell scale-up via electrochemistry-, hydrodynamic-, and microbial ecology-informed framework

Microbial electrolysis cells (MECs) can produce green hydrogen while removing organic contaminants from liquid waste streams by leveraging the metabolic activity of electroactive microorganisms. Despite their potential in a sustainable, circular economy, large-scale MECs that can treat relevant volumes of wastewater have failed to deliver performance proportional to their lab-scale counterparts. The reason behind this lower performance at scale remains unclear. Here, in this study, we developed a combined electrochemistry-, hydrodynamic-, and microbial ecology-informed framework to analyze and optimize MEC performance during scale-up, enabling accurate quantification of major limitations and the identification of strategies to overcome them, ultimately facilitating equivalent performance at scale. Applying this framework to the scale-up of a zero-gap MEC from 9 cm 2 electrode area to 100 cm 2 electrode area, resulted in similar maximum current densities in a 100 cm 2 MEC (21.7 ± 1.1 A/m 2 ) compared to a 9 cm 2 system (25.1 ± 2.7 A/m 2 ), as well as equivalent hydrogen production rates of 69.3 L/L-d (100 cm 2 ) and 67.7 ± 2.4 L/L-d (9 cm 2 ). COMSOL flow dynamics simulations were used to scale up the reactor configuration without negatively affecting electrolyte velocity and distribution in the cell, minimizing the increase in internal resistances during scale-up (11.7 ± 0.5 mΩm 2 at 9 cm 2 ; 19.7 ± 1.3 mΩm 2 at 100 cm 2 ). Microbial community structures were assessed at both scales using high-throughput sequencing, highlighting the differences of populations across electrode dimensions and operational parameters. The framework presented here accelerates the development of effective strategies toward the scale-up of MECs by furthering the understanding of how electrochemical, hydrodynamic, and microbial ecology parameters change as the reactor dimension is increased. Ultimately, this approach contributes to advancing electrochemical biotechnology toward practical deployment in energy-efficient wastewater treatment systems.

Flow path↗
DOE OSTI2019

The spatial scale dependence of diazotrophic and bacterial community assembly in paddy soil

Aim: The factors driving microbial community β-diversity (variation in composition) at different spatial scales yield fundamental insights into the mechanisms that maintain ecosystem biodiversity, which as yet are uncertain. In this work, we explore whether spatial scale-dependent patterns of β-diversity vary between microbial functional groups and bacterial taxa (i.e., diazotrophic and bacterial communities) across local to regional scales (from metres to hundreds of kilometres). Location: Eastern China. Time period: October and November 2015. Major taxa studied: Diazotrophic and bacterial communities. Methods: We use two complementary statistical tools to unveil biotic mechanisms (i.e., species association) underlying variation in β-diversity of diazotrophic and bacterial communities. We examined distance–decay slopes of both communities at the local (1–113 m), meso- (3.4–39 km) and regional (103–668 km) scales. We used an environmentally constrained checkerboard score and topological features of association networks as indices of species association. We then calculated contributions of species association, abiotic factors and geographical distance to explain community β-diversity. The scale-dependent distance–decay relationships were also examined in ubiquitous (high occupancy across samples) and endemic communities of diazotrophs and bacteria. Results: Diazotrophs displayed steeper distance–decay slopes than bacteria, suggesting that the β-diversity of diazotrophic communities was more variable. The distance–decay slopes were dependent on spatial scales in both communities, owing to different contributions of geographical distance, abiotic factors and species association at three spatial scales. Intriguingly, species association was greater and contributed more to community β-diversity than other forces at the local scale, implying that species association could greatly alter community structures. Main conclusions: Drivers of diazotrophic and bacterial community β-diversity depended on spatial scales, resulting in different distance–decay patterns. Moreover, this was the first study to use two methods to demonstrate that species association played important, but as yet unrecognized, roles in driving spatial scale-dependent β-diversity.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

A New Modeling Framework for Multi-Scale Simulation of Hydraulic Fracturing and Production from Unconventional Reservoirs

This paper describes a new modeling framework for microscopic to reservoir-scale simulations of hydraulic fracturing and production. The approach builds upon a fusion of two existing high-performance simulators for reservoir-scale behavior: the GEOS code for hydromechanical evolution during stimulation and the TOUGH+ code for multi-phase flow during production. The reservoir-scale simulations are informed by experimental and modeling studies at the laboratory scale to incorporate important micro-scale mechanical processes and chemical reactions occurring within the fractures, the shale matrix, and at the fracture-fluid interfaces. These processes include, among others, changes in stimulated fracture permeability as a result of proppant behavior rearrangement or embedment, or mineral scale precipitation within pores and microfractures, at µm to cm scales. In our new modeling framework, such micro-scale testing and modeling provides upscaled hydromechanical parameters for the reservoir scale models. We are currently testing the new modeling framework using field data and core samples from the Hydraulic Fracturing Field Test (HFTS), a recent field-based joint research experiment with intense monitoring of hydraulic fracturing and shale production in the Wolfcamp Formation in the Permian Basin (USA). Below, we present our approach coupling the reservoir simulators GEOS and TOUGH+ informed by upscaled parameters from micro-scale experiments and modeling. We provide a brief overview of the HFTS and the available field data, and then discuss the ongoing application of our new workflow to the HFTS data set.

58 GEOSCIENCES↗
DOE OSTI2021

Hierarchical Fractional Advection-Dispersion Equation (FADE) to Quantify Anomalous Transport in River Corridor over a Broad Spectrum of Scales: Theory and Applications

Fractional calculus-based differential equations were found by previous studies to be promising tools in simulating local-scale anomalous diffusion for pollutants transport in natural geological media (geomedia), but efficient models are still needed for simulating anomalous transport over a broad spectrum of scales. This study proposed a hierarchical framework of fractional advection-dispersion equations (FADEs) for modeling pollutants moving in the river corridor at a full spectrum of scales. Applications showed that the fixed-index FADE could model bed sediment and manganese transport in streams at the geomorphologic unit scale, whereas the variable-index FADE well fitted bedload snapshots at the reach scale with spatially varying indices. Further analyses revealed that the selection of the FADEs depended on the scale, type of the geomedium (i.e., riverbed, aquifer, or soil), and the type of available observation dataset (i.e., the tracer snapshot or breakthrough curve (BTC)). When the pollutant BTC was used, a single-index FADE with scale-dependent parameters could fit the data by upscaling anomalous transport without mapping the sub-grid, intermediate multi-index anomalous diffusion. Pollutant transport in geomedia, therefore, may exhibit complex anomalous scaling in space (and/or time), and the identification of the FADE’s index for the reach-scale anomalous transport, which links the geomorphologic unit and watershed scales, is the core for reliable applications of fractional calculus in hydrology.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

On the scaling of wind turbine rotors

This paper formulates laws for scaling wind turbine rotors. Although the analysis is general, the article primarily focuses on the subscaling problem, i.e., on the design of a smaller-sized model that mimics a full-scale machine. The present study considers both the steady-state and transient response cases, including the effects of aerodynamic, elastic, inertial, and gravitational forces. The analysis reveals the changes to physical characteristics induced by a generic change of scale, indicates which characteristics can be matched faithfully by a subscaled model, and states the conditions that must be fulfilled for desired matchings to hold. Based on the scaling laws formulated here, the article continues by considering the problem of designing scaled rotors that match desired indicators of a full-scale reference. To better illustrate the challenges implicit in scaling and the necessary tradeoffs and approximations, two different approaches are contrasted. The first consists in a straightforward geometric zooming. An analysis of the consequences of zooming reveals that, although apparently simple, this method is often not applicable in practice, because of physical and manufacturing limitations. This motivates the formulation of scaling as a constrained optimal aerodynamic and structural matching problem of wide applicability. Practical illustrations are given considering the scaling of a large reference 10 MW wind turbine of about 180 m in diameter down to three different sizes of 54, 27, and 2.8 m. Results indicate that, with the proper choices, even models characterized by very significant scaling factors can accurately match several key performance indicators. Additionally, when an exact match is not possible, relevant trends can at least be captured.

17 WIND ENERGY↗
DOE OSTI2022

Scaling and adiabaticity in a rapidly expanding gluon plasma

In this work we aim to gain qualitative insight on the far-from-equilibrium behavior of the gluon plasma produced in the early stages of a heavy-ion collision. It was recently discovered [1] that the distribution functions of quarks and gluons in QCD effective kinetic theory (EKT) exhibit self-similar “scaling” evolution with time-dependent scaling exponents long before those exponents reach their pre-hydrodynamic fixed-point values. In this work we shed light on the origin of this time-dependent scaling phenomenon in the small-angle approximation to the Boltzmann equation. We first solve the Boltzmann equation numerically and find that time-dependent scaling is a feature of this kinetic theory, and that it captures key qualitative features of the scaling of hard gluons in QCD EKT. We then proceed to study scaling analytically and semi-analytically in this equation. We find that an appropriate momentum rescaling allows the scaling distribution to be identified as the instantaneous ground state of the operator describing the evolution of the distribution function, and the approach to the scaling function is described by the decay of the excited states. That is to say, there is a frame in which the system evolves adiabatically. Furthermore, from the conditions for adiabaticity we can derive evolution equations for the time-dependent scaling exponents. In addition to the known free-streaming and BMSS fixed points, we identify a new “dilute” fixed point when the number density becomes small before hydrodynamization. Corrections to the fixed point exponents in the small-angle approximation agree quantitatively with those found previously in QCD EKT and arise from the evolution of the ratio between hard and soft scales.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

A comparative analysis of numerical approaches for the description of gas flow in clay-based repository systems: From a laboratory to a large-scale gas injection test

There is nowadays a consensus among many countries that geological disposal is a favourable solution for the long-term management. Although different host formations and different barrier systems are under consideration around the world, clay-based materials form an important component for waste isolation in most national programmes. Hence, a good comprehension of the effect of gas flow on the hydro-mechanical behaviour of clay-based soils is essential, both at laboratory and field scale. Task B under the international cooperative project DECOVALEX-2023 has recently shown that, after some enhancement, models can be employed to reproduce laboratory scale tests, even with different sample geometries 37 . However, further work is required to understand whether they can be applied to simulate a large-scale experiment. Up-scaling of models for the advective transport of gas through clay-based low permeable material presents a number of problems related to the difficulty in obtaining consistent hydrogeological parameters and constitutive relationships at both laboratory and field scale. Based on a unique dataset from a large-scale gas injection test (Lasgit) performed at the Äspö Hard Rock Laboratory (Sweden), Task B within DECOVALEX-2023 has explored the refinement of these numerical strategies applied to the simulation of gas flow. Work performed within the task reveals that codes do not need to be substantially modified from the laboratory models to reproduce full-scale tests: indeed, model parameters calibrated and validated at laboratory scale have been applied to predict field scale gas flow at Lasgit, including peak gas pressure and injected cumulative gas volume. By means of (1) the introduction of interfaces between blocks to reflect the experimental configuration and the (2) adjustment of some parameters (e.g., higher permeability), the updated models are able to represent most of the key features observed in the experimental data, even at a large scale.

Tamayo-Mas, E↗
DOE OSTI2022

Dual-scale folding in cutting of commercially pure aluminum alloys

We examine a, hitherto, little-studied and curious machining chip morphology, with tell-tale signs of folding at two different length scales, that is common in cutting of certain ductile and highly strain-hardening metals like soft aluminum alloys, tantalum and niobium. This chip morphology does not appear in the usual catalogues of common chip types. The mechanics of formation of the “dual-scale folded chip” is studied in model material systems of commercially pure aluminum alloys (AA 1100 and AA 8040), that prominently exhibit this chip morphology. The flow, folding and associated plastic instabilities are investigated using micro/macro structure observations of the chip in a plane-strain cutting framework, with high-speed in situ imaging and image analysis of material flow; and force measurements. The smaller-scale folding is shown to develop in the primary deformation zone while the larger-scale folding occurs as the chip traverses the rake face of the tool. The resulting chip is composed of irregularly-spaced large folds, superimposed onto which are the quasi periodic small folds. The representative wavelengths of the two folds differ on average by an order of magnitude, 0.1 mm vs. 2 mm. The observations reveal a direct coupling between the material flow and chip morphology, and how specific attributes of the dual-scale folded chip arise from the flow mechanism. Plastic buckling is found to play a key role in the folding at both length scales. The small-scale folds are characteristic of a sinuous plastic flow mode, while the large-scale folding is characterized by buckling and stick-slip along the tool rake face, triggered by adhesive pinning of the chip to the tool. Important consequences of the dualscale folding are very large cutting forces, and force oscillations of large amplitude, despite the alloys being very soft, only ~ 25 HV. Here, the dual-scale folding is why many of these alloys are classified as “gummy” to machine. Since the dual-scale folded chip is associated with large cutting forces and poor surface quality, there is much to be gained by disrupting this flow type in practical machining applications. Methods for controlling the folding to improve machining performance with the gummy alloys are briefly discussed.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Determining Spatial Scales of Soil Moisture—Cloud Coupling Pathways Using Semi-Idealized Simulations

The spatial scales of land-atmosphere interactions over heterogeneous, realistic soil moisture patterns are critical to improve our understanding of land-atmosphere interactions. However, these scales are poorly quantified. We use high-resolution numerical experiments to quantify the spatial scales for a selected day during the Holistic Interactions of Shallow Clouds, Aerosols, and Land-Ecosystems (HI-SCALE) campaign in Oklahoma. A semi-idealized approach (removing background winds and surface topography while retaining the real-world data for other boundary conditions) enables examination of the local influence from the surface. Simulations that apply uniform surface, variable land cover with uniform soil moisture, and variable land cover with variable soil moisture are then compared. Land cover variations, especially water and urban surfaces, create two variance peaks in the surface sensible heat flux in the scales >10 km (meso-β) and <6 km (meso-γ). Both peaks are enhanced by the observation-based soil moisture distribution that has most of its variance in the meso-β scale. Atmospheric response in the meso-β scale is hydrostatic with weak vertical motion. The land cover variations induce secondary circulations in the scales of 2.5–6 km. The additional soil moisture variability intensifies extreme circulations over dry soil patches and sharp sensible heat flux gradients, slightly extending the characteristic scales to 2.5–9 km. While their areal coverage is small, soil moisture variations on such “hotspots” lead to substantially larger convective cloud structure and domain-mean rainfall, calling for a consideration of their non-linear effect in large-scale models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Scaling of the mean transverse flow and Reynolds shear stress in turbulent plane jet

Here, proper scaling for the mean transverse flow and Reynolds shear stress in a turbulent plane jet is determined using a scaling patch approach. By seeking an admissible scaling, a key concept in the scaling patch approach, for the mean continuity equation, a proper scale for the mean transverse flow in a turbulent plane jet is found as V ref = –δdU ctr /dx, where δ is the jet half width and dU ctr /dx is the decay rate of the mean axial velocity at the jet centerline. By seeking an admissible scaling for the mean axial momentum equation, a proper scale for the kinematic Reynolds shear stress is found as R uv,ref =U ctr V ref , which is a mix of the velocity scales in the axial and transverse directions. Approximation functions for the scaled mean transverse flow and Reynolds shear stress are developed and found to agree well with experimental and numerical data. Similarities and differences between the scales of the mean transverse flow and Reynolds shear stress in turbulent plane jets and zero-pressure-gradient turbulent boundary layer flows are clarified.

42 ENGINEERING↗
DOE OSTI2026

Hierarchical-embedding autoencoder with a predictor as efficient architecture for learning time-evolution in multi-scale turbulent flows

We introduce a scale-aware, data-driven deep learning modeling framework for accurately predicting the time evolution of multi-scale turbulent plasma and liquid flows. The approach is motivated by the idea of scale separation. Structures of vastly different length scales emerge in these systems, and interactions between these structures occur only locally. To exploit this structure, the flow state is transformed by a hierarchical, fully convolutional autoencoder, not into a single embedding layer as in conventional convolutional surrogate models, but into a series of embedding layers. A stepwise training strategy ensures that fine-scale features are encoded on a high-resolution grid, while larger structures are represented on progressively coarser layers. The time evolution predictor advances all embedding layers in sync, capturing local interactions between features at the same scale as well as between all scales. This approach enables efficient modeling of multi-scale systems since negligible interactions between distant, small-scale structures do not need to be directly modeled. Our hierarchical-embedding autoencoder with a predictor framework is evaluated on canonical examples of multi-scale turbulence: two-dimensional Kolmogorov flow and Hasegawa–Wakatani plasma turbulence. In both cases, the proposed framework significantly improves predictive accuracy relative to conventional convolutional network architectures. A significant improvement in prediction accuracy was observed for crucial statistical characteristics of the Hasegawa–Wakatani plasma as well as for individual trajectories of the Kolmogorov flow turbulence. Importantly, the model's rollout for the Hasegawa–Wakatani problem demonstrates a four-order-of-magnitude speedup compared to traditional numerical solvers.

Khrabry, Alexander I. [Princeton Univ., NJ (United↗
DOE OSTI2014

The role of subsurface flows in solar surface convection: modeling the spectrum of supergranular and larger scale flows

We model the solar horizontal velocity power spectrum at scales larger than granulation using a two-component approximation to the mass continuity equation. The model takes four times the density scale height as the integral (driving) scale of the vertical motions at each depth. Scales larger than this decay with height from the deeper layers. Those smaller are assumed to follow a Kolmogorov turbulent cascade, with the total power in the vertical convective motions matching that required to transport the solar luminosity in a mixing length formulation. These model components are validated using large-scale radiative hydrodynamic simulations. We reach two primary conclusions. (1) The model predicts significantly more power at low wavenumbers than is observed in the solar photospheric horizontal velocity spectrum. (2) Ionization plays a minor role in shaping the observed solar velocity spectrum by reducing convective amplitudes in the regions of partial helium ionization. The excess low wavenumber power is also seen in the fully nonlinear three-dimensional radiative hydrodynamic simulations employing a realistic equation of state. This adds to other recent evidence suggesting that the amplitudes of large-scale convective motions in the Sun are significantly lower than expected. Employing the same feature tracking algorithm used with observational data on the simulation output, we show that the observed low wavenumber power can be reproduced in hydrodynamic models if the amplitudes of large-scale modes in the deep layers are artificially reduced. Since the large-scale modes have reduced amplitudes, modes on the scale of supergranulation and smaller remain important to convective heat flux even in the deep layers, suggesting that small-scale convective correlations are maintained through the bulk of the solar convection zone.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2016

Large-scale dynamo action precedes turbulence in shearing box simulations of the magnetorotational instability

Here, we study the dynamo generation (exponential growth) of large-scale (planar averaged) fields in unstratified shearing box simulations of the magnetorotational instability (MRI). In contrast to previous studies restricted to horizontal (x–y) averaging, we also demonstrate the presence of large-scale fields when vertical (y–z) averaging is employed instead. By computing space–time planar averaged fields and power spectra, we find large-scale dynamo action in the early MRI growth phase – a previously unidentified feature. Non-axisymmetric linear MRI modes with low horizontal wavenumbers and vertical wavenumbers near that of expected maximal growth, amplify the large-scale fields exponentially before turbulence and high wavenumber fluctuations arise. Thus the large-scale dynamo requires only linear fluctuations but not non-linear turbulence (as defined by mode–mode coupling). Vertical averaging also allows for monitoring the evolution of the large-scale vertical field and we find that a feedback from horizontal low wavenumber MRI modes provides a clue as to why the large-scale vertical field sustains against turbulent diffusion in the non-linear saturation regime. We compute the terms in the mean field equations to identify the individual contributions to large-scale field growth for both types of averaging. The large-scale fields obtained from vertical averaging are found to compare well with global simulations and quasi-linear analytical analysis from a previous study by Ebrahimi & Blackman. We discuss the potential implications of these new results for understanding the large-scale MRI dynamo saturation and turbulence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Renormalization scale setting for heavy quark pair production in $e^+e^–$ annihilation near the threshold region

Heavy fermion pair production in e + e – annihilation is a fundamental process in hadron physics and is of considerable interest for various phenomena. In this paper, we will apply the principle of maximum conformality (PMC) to provide a comprehensive analysis of these processes. The PMC provides a systematic, unambiguous method for determining the renormalization scales of the QCD coupling constant for single-scale and multiple-scale applications. The resulting predictions eliminate any renormalization scheme-and-scale ambiguities, eliminate the factorial renormalon divergences, and are consistent with the requirements of the renormalization group. It is remarkable that two distinctly different scales are determined by using the PMC for heavy fermion pair production near the threshold region. One scale is the order of the fermion mass m f , which enters the hard virtual corrections, and the other scale is of order v m f , where v is the quark velocity, which enters the Coulomb rescattering amplitude. The PMC scales yield the correct physical behavior and reflect the virtuality of the propagating gluons (photons) for the QCD (QED) processes. Moreover, we demonstrate the consistency of PMC scale setting from QCD to QED. Perfect agreement between the Abelian unambiguous Gell-Mann-Low and the PMC scale-setting methods in the limit of zero number of colors is demonstrated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗