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LAMP Emittance Budget, Rev. 1

This report summarizes the performance limits of the LANSCE Coupled-Cavity Linac (CCL). These results are captured or summarized directly from the references cited. This report was written in support of the LANSCE Modernization Project (LAMP). This brief report summarizes the emittance budget for the LANSCE Modernization Project (LAMP). While the project Key Performance Parameters (KPPs) specify threshold and objective requirements for charge delivered to each experimental area, no upper limits on beam emittances are specified. To maintain low losses in the high-energy section of the LANSCE linac and hands-on maintenance, some upper limits on beam emittance need to be specified for the new LAMP front-end performance. The scope of the LAMP project replaces the injector section and drift-tube linac (DTL) up to 100 MeV of the existing LANSCE linac. This new design replacement will be integrated with the remaining coupled cavity linac (CCL) which makes up most of the accelerator at LANSCE and accelerates the beam to a final energy of 800 MeV. The initial approach that has been used to define an emittance budget for the new LAMP front end is based on recent and historical measured beam emittances at 100 MeV for the three beam types accelerated at LANSCE: H+ (protons for isotope production), LBEG (H- beam for delivery to proton radiography and to the Lujan neutron spallation target, and MPEG (H- beam for delivery to the Weapons Neutron Research facility). The emittance budget (upper limit) for each beam type has been selected to maintain the losses in the CCL to a level approximately equivalent to those observed in present operations to first order. However, the goal of the LAMP project is to improve the quality of the beams injected into the CCL, if possible, thus allowing for higher average current operation while also lowering beam losses and activation at high beam energies. The table below summarizes the beam measurements evaluated and used to establish a conservative emittance budget for LAMP based on known historical beam losses and activation. However, based on estimates of the CCL admittance and the Isotope Production Facility (IPF) beamline acceptance, a more relaxed transverse emittance upper limit of 0.095 π-cm-mrad, rms, normalized may be acceptable at 100 MeV while still meeting the LAMP performance requirements for charge delivery to each LANSCE experimental area and maintaining hands-on maintenance. This upper limit is supported by a recent analysis of operational data. Additionally, the present conceptual LAMP front-end design meets this requirement.

43 PARTICLE ACCELERATORS↗

Global Carbon Budget 2021

Abstract. Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize datasets and methodology to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO2 sink (SLAND) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the first time, an approach is shown to reconcile the difference in our ELUC estimate with the one from national greenhouse gas inventories, supporting the assessment of collective countries' climate progress. For the year 2020, EFOS declined by 5.4 % relative to 2019, with fossil emissions at 9.5 ± 0.5 GtC yr−1 (9.3 ± 0.5 GtC yr−1 when the cement carbonation sink is included), and ELUC was 0.9 ± 0.7 GtC yr−1, for a total anthropogenic CO2 emission of 10.2 ± 0.8 GtC yr−1 (37.4 ± 2.9 GtCO2). Also, for 2020, GATM was 5.0 ± 0.2 GtC yr−1 (2.4 ± 0.1 ppm yr−1), SOCEAN was 3.0 ± 0.4 GtC yr−1, and SLAND was 2.9 ± 1 GtC yr−1, with a BIM of −0.8 GtC yr−1. The global atmospheric CO2 concentration averaged over 2020 reached 412.45 ± 0.1 ppm. Preliminary data for 2021 suggest a rebound in EFOS relative to 2020 of +4.8 % (4.2 % to 5.4 %) globally. Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2020, but discrepancies of up to 1 GtC yr−1 persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use changes emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extra-tropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and datasets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this dataset (Friedlingstein et al., 2020, 2019; Le Quéré et al., 2018b, a, 2016, 2015b, a, 2014, 2013). The data presented in this work are available at https://doi.org/10.18160/gcp-2021 (Friedlingstein et al., 2021).

Friedlingstein, Pierre (ORCID:0000000333094739)↗

Global Carbon Budget 2022

Abstract. Accurate assessment of anthropogenic carbon dioxide (CO2) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere in a changing climate is critical to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe and synthesize data sets and methodologies to quantify the five major components of the global carbon budget and their uncertainties. Fossil CO2 emissions (EFOS) are based on energy statistics and cement production data, while emissions from land-use change (ELUC), mainly deforestation, are based on land use and land-use change data and bookkeeping models. Atmospheric CO2 concentration is measured directly, and its growth rate (GATM) is computed from the annual changes in concentration. The ocean CO2 sink (SOCEAN) is estimated with global ocean biogeochemistry models and observation-based data products. The terrestrial CO2 sink (SLAND) is estimated with dynamic global vegetation models. The resulting carbon budget imbalance (BIM), the difference between the estimated total emissions and the estimated changes in the atmosphere, ocean, and terrestrial biosphere, is a measure of imperfect data and understanding of the contemporary carbon cycle. All uncertainties are reported as ±1σ. For the year 2021, EFOS increased by 5.1 % relative to 2020, with fossil emissions at 10.1 ± 0.5 GtC yr−1 (9.9 ± 0.5 GtC yr−1 when the cement carbonation sink is included), and ELUC was 1.1 ± 0.7 GtC yr−1, for a total anthropogenic CO2 emission (including the cement carbonation sink) of 10.9 ± 0.8 GtC yr−1 (40.0 ± 2.9 GtCO2). Also, for 2021, GATM was 5.2 ± 0.2 GtC yr−1 (2.5 ± 0.1 ppm yr−1), SOCEAN was 2.9 ± 0.4 GtC yr−1, and SLAND was 3.5 ± 0.9 GtC yr−1, with a BIM of −0.6 GtC yr−1 (i.e. the total estimated sources were too low or sinks were too high). The global atmospheric CO2 concentration averaged over 2021 reached 414.71 ± 0.1 ppm. Preliminary data for 2022 suggest an increase in EFOS relative to 2021 of +1.0 % (0.1 % to 1.9 %) globally and atmospheric CO2 concentration reaching 417.2 ppm, more than 50 % above pre-industrial levels (around 278 ppm). Overall, the mean and trend in the components of the global carbon budget are consistently estimated over the period 1959–2021, but discrepancies of up to 1 GtC yr−1 persist for the representation of annual to semi-decadal variability in CO2 fluxes. Comparison of estimates from multiple approaches and observations shows (1) a persistent large uncertainty in the estimate of land-use change emissions, (2) a low agreement between the different methods on the magnitude of the land CO2 flux in the northern extratropics, and (3) a discrepancy between the different methods on the strength of the ocean sink over the last decade. This living data update documents changes in the methods and data sets used in this new global carbon budget and the progress in understanding of the global carbon cycle compared with previous publications of this data set. The data presented in this work are available at https://doi.org/10.18160/GCP-2022 (Friedlingstein et al., 2022b).

54 ENVIRONMENTAL SCIENCES↗

Global Carbon Budget 2015

Accurate assessment of anthropogenic carbon dioxide (CO 2 ) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and a methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics, and model estimates and their interpretation by a broad scientific community. We also discuss changes compared to previous estimates as well as consistency within and among components, alongside methodology and data limitations. CO 2 emissions from fossil fuels and industry ( E FF ) are based on energy statistics and cement production data, while emissions from land-use change ( E LUC ), mainly deforestation, are based on combined evidence from land-cover-change data, fire activity associated with deforestation, and models. The global atmospheric CO 2 concentration is measured directly and its rate of growth ( G ATM ) is computed from the annual changes in concentration. Moreover, the mean ocean CO 2 sink ( S OCEAN ) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in S OCEAN is evaluated with data products based on surveys of ocean CO 2 measurements. The global residual terrestrial CO 2 sink ( S LAND ) is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models forced by observed climate, CO 2 , and land-cover change (some including nitrogen–carbon interactions). We compare the mean land and ocean fluxes and their variability to estimates from three atmospheric inverse methods for three broad latitude bands. All uncertainties are reported as ±1σ, reflecting the current capacity to characterise the annual estimates of each component of the global carbon budget. For the last decade available (2005–2014), E FF was 9.0 ± 0.5 GtC yr -1 , E LUC was 0.9 ± 0.5 GtC yr -1 , G ATM was 4.4 ± 0.1 GtC yr -1 , S OCEAN was 2.6 ± 0.5 GtC yr -1 , and S LAND was 3.0 ± 0.8 GtC yr -1 . For the year 2014 alone, E FF grew to 9.8 ± 0.5 GtC yr -1 , 0.6 % above 2013, continuing the growth trend in these emissions, albeit at a slower rate compared to the average growth of 2.2 % yr -1 that took place during 2005–2014. Also, for 2014, E LUC was 1.1 ± 0.5 GtC yr -1 , G ATM was 3.9 ± 0.2 GtC yr -1 , S OCEAN was 2.9 ± 0.5 GtC yr -1 , and S LAND was 4.1 ± 0.9 GtC yr -1 . G ATM was lower in 2014 compared to the past decade (2005–2014), reflecting a larger S LAND for that year. The global atmospheric CO 2 concentration reached 397.15 ± 0.10 ppm averaged over 2014. For 2015, preliminary data indicate that the growth in E FF will be near or slightly below zero, with a projection of -0.6 [range of -1.6 to +0.5] %, based on national emissions projections for China and the USA, and projections of gross domestic product corrected for recent changes in the carbon intensity of the global economy for the rest of the world. From this projection of E FF and assumed constant E LUC for 2015, cumulative emissions of CO 2 will reach about 555 ± 55 GtC (2035 ± 205 GtCO 2 ) for 1870–2015, about 75 % from E FF and 25 % from E LUC . Finally, this living data update documents changes in the methods and data sets used in this new carbon budget compared with previous publications of this data set (Le Quéré et al., 2015, 2014, 2013). All observations presented here can be downloaded from the Carbon Dioxide Information Analysis Center ( doi:10.3334/CDIAC/GCP_2015 ).

54 ENVIRONMENTAL SCIENCES↗

Global carbon budget 2014

Accurate assessment of anthropogenic carbon dioxide (CO 2 ) emissions and their redistribution among the atmosphere, ocean, and terrestrial biosphere is important to better understand the global carbon cycle, support the development of climate policies, and project future climate change. Here we describe data sets and a methodology to quantify all major components of the global carbon budget, including their uncertainties, based on the combination of a range of data, algorithms, statistics, and model estimates and their interpretation by a broad scientific community. We discuss changes compared to previous estimates, consistency within and among components, alongside methodology and data limitations. CO 2 emissions from fossil fuel combustion and cement production ( E FF ) are based on energy statistics and cement production data, respectively, while emissions from land-use change ( E LUC ), mainly deforestation, are based on combined evidence from land-cover-change data, fire activity associated with deforestation, and models. The global atmospheric CO 2 concentration is measured directly and its rate of growth ( G ATM ) is computed from the annual changes in concentration. The mean ocean CO 2 sink ( S OCEAN ) is based on observations from the 1990s, while the annual anomalies and trends are estimated with ocean models. The variability in S OCEAN is evaluated with data products based on surveys of ocean CO 2 measurements. The global residual terrestrial CO 2 sink ( S LAND ) is estimated by the difference of the other terms of the global carbon budget and compared to results of independent dynamic global vegetation models forced by observed climate, CO 2 , and land-cover-change (some including nitrogen–carbon interactions). We compare the mean land and ocean fluxes and their variability to estimates from three atmospheric inverse methods for three broad latitude bands. All uncertainties are reported as ±1σ;, reflecting the current capacity to characterise the annual estimates of each component of the global carbon budget. For the last decade available (2004–2013), E FF was 8.9 ± 0.4 GtC yr⁻¹, E LUC 0.9 ± 0.5 GtC yr⁻¹, G ATM 4.3 ± 0.1 GtC yr⁻¹, S OCEAN 2.6 ± 0.5 GtC yr⁻¹, and S LAND 2.9 ± 0.8 GtC yr⁻¹. For year 2013 alone, E FF grew to 9.9 ± 0.5 GtC yr⁻¹, 2.3% above 2012, continuing the growth trend in these emissions, E LUC was 0.9 ± 0.5 GtC yr⁻¹, G ATM was 5.4 ± 0.2 GtC yr⁻¹, S OCEAN was 2.9 ± 0.5 GtC yr⁻¹, and S LAND was 2.5 ± 0.9 GtC yr⁻¹. G ATM was high in 2013, reflecting a steady increase in E FF and smaller and opposite changes between S OCEAN and S LAND compared to the past decade (2004–2013). The global atmospheric CO 2 concentration reached 395.31 ± 0.10 ppm averaged over 2013. We estimate that E FF will increase by 2.5% (1.3–3.5%) to 10.1 ± 0.6 GtC in 2014 (37.0 ± 2.2 GtCO 2 yr⁻¹), 65% above emissions in 1990, based on projections of world gross domestic product and recent changes in the carbon intensity of the global economy. From this projection of E FF and assumed constant E LUC for 2014, cumulative emissions of CO 2 will reach about 545 ± 55 GtC (2000 ± 200 GtCO 2 ) for 1870–2014, about 75% from E FF and 25% from E LUC . This paper documents changes in the methods and data sets used in this new carbon budget compared with previous publications of this living data set (Le Quéré et al., 2013, 2014). All observations presented here can be downloaded from the Carbon Dioxide Information Analysis Center ( doi:10.3334/CDIAC/GCP_2014 ).

54 ENVIRONMENTAL SCIENCES↗

Kinetic energy budgets in areas of convection

Synoptic scale budgets of kinetic energy are computed using 3 and 6 h data from three of NASA's Atmospheric Variability Experiments (AVE's). Numerous areas of intense convection occurred during the three experiments. Large kinetic energy variability, with periods as short as 6 h, is observed in budgets computed over each entire experiment area and over limited volumes that barely enclose the convection and move with it. Kinetic energy generation and transport processes in the smaller volumes are often a maximum when the enclosed storms are near peak intensity, but the nature of the various energy processes differs between storm cases and seems closely related to the synoptic conditions. A commonly observed energy budget for peak storm intensity indicates that generation of kinetic energy by cross-contour flow is the major energy source while dissipation to subgrid scales is the major sink. Synoptic scale vertical motion transports kinetic energy from lower to upper levels of the atmosphere while low-level horizontal flux convergence and upper-level horizontal divergence also occur. Spatial fields of the energy budget terms show that the storm environment is a major center of energy activity for the entire area.

Fuelberg, H. E.↗

System implementation for earth radiation budget satellite system

The earth-orbiting satellite provides a platform, outside the earth's atmosphere, which is capable of simultaneously monitoring the outgoing reflection of the sun's energy from the earth's surface and atmosphere, and the longwave radiation emitted by the earth and its atmosphere. These capabilities provide the opportunity to conduct detailed studies of the variations in the earth's radiation budget, the effects of natural and manmade changes in the environment on this budget, and the effects which changes in the energy budget produce on earth's weather and climate. A description is presented of the instrument system requirements and a conceptual design of an instrument approach to meet these requirements for providing the earth radiation budget data.

Cooper, J. E.↗

Satellite measurements of earth radiation budget for climate applications

Understanding the global balance between the absorption of solar radiation and the emission of longwave radiation is considered pivotal to understanding the processes which govern the earth's climate. In concert with a large scientific community interested in the earth's radiation budget, NASA has initiated a program to accurately determine the spatial and temporal characteristics of the earth's radiation budget. This program will utilize instrumentation placed on three satellites including the Space Shuttle-launched free flying Earth Radiation Budget Satellite. The program is discussed relative to its scientific background, plans for the Earth Radiation Budget Experiment, and the relationship of this effort to present and future climate research activities.

Curran, R. J.↗

Kinetic energy budget during strong jet stream activity over the eastern United States

Kinetic energy budgets are computed during a cold air outbreak in association with strong jet stream activity over the eastern United States. The period is characterized by large generation of kinetic energy due to cross-contour flow. Horizontal export and dissipation of energy to subgrid scales of motion constitute the important energy sinks. Rawinsonde data at 3 and 6 h intervals during a 36 h period are used in the analysis and reveal that energy fluctuations on a time scale of less than 12 h are generally small even though the overall energy balance does change considerably during the period in conjunction with an upper level trough which moves through the region. An error analysis of the energy budget terms suggests that this major change in the budget is not due to random errors in the input data but is caused by the changing synoptic situation. The study illustrates the need to consider the time and space scales of associated weather phenomena in interpreting energy budgets obtained through use of higher frequency data.

Fuelberg, H. E.↗

Simulation of a numerical filter for enhancing earth radiation budget measurements

The Earth Radiation Budget Experiment has the objective to collect the radiation budget data which are needed to determine the radiation budget at the top of the atmosphere (TOA) on a regional scale. A second objective is to determine the accuracy of the results. Three satellites will carry wide and medium field of view radiometers which measure the longwave and shortwave components of radiation. Scanning radiometers will be included to detect small spatial features. A proposal has been made to employ for the nonscanning radiometers a one-dimensional numerical filter which reduces satellite measurements to TOA radiant excitances. The numerical filter was initially formulated by House (1980). It enhances the resolution of the radiation budget along the satellite groundtrack. The accuracy of the numerical filter estimate is studied by simulating the data gathering and measurement inversion process. The results of the study are discussed, taking into account two error sources.

Green, R. N.↗

Radiation budget measurement/model interface

This final report includes research results from the period February, 1981 through November, 1982. Two new results combine to form the final portion of this work. They are the work by Hanna (1982) and Stevens to successfully test and demonstrate a low-order spectral climate model and the work by Ciesielski et al. (1983) to combine and test the new radiation budget results from NIMBUS-7 with earlier satellite measurements. Together, the two related activities set the stage for future research on radiation budget measurement/model interfacing. Such combination of results will lead to new applications of satellite data to climate problems. The objectives of this research under the present contract are therefore satisfied. Additional research reported herein includes the compilation and documentation of the radiation budget data set a Colorado State University and the definition of climate-related experiments suggested after lengthy analysis of the satellite radiation budget experiments.

Vonderhaar, T. H.↗

Design concept for an optimized earth radiation budget sensor

The Earth Radiation Budget Program has the objective to measure and model the terrestrial radiation budget and obtain a better understanding of the climate and its changes. A multisensor, multisatellite system with high and midinclination orbits will be needed for implementing this program. Various approaches for conducting sensing operations have been evaluated. The present investigation considers a method of sampling with a unique multidirectional array mosaic sensor to fulfill the requirements of earth radiation budget measurements. Previous and present generation earth radiation budget (ERB) satellite instruments are discussed, and attention is given to instrument design tradeoffs and the baseline instrument concept.

Carman, S. L.↗

Accuracy of diagnostic heat and moisture budgets using SESAME-79 field data as revealed by observing system simulation experiments

Observing system simulation experiments are used to investigate the accuracy of diagnostic heat and moisture budgets which employ the AVE-SESAME 1979 data. The time-including, four-dimensional data set of a mesoscale model is used to simulate rawinsonde observations from AVE-SESAME 1979. The 5 C/day (heat budget) and 2 g/kg per day (moisture budget) magnitudes of error obtained indicate difficulties in the diagnosis of the heating rate in weak convective systems. The influences exerted by observational frequency, objective analysis, observational density, vertical interpolation, and observational errors on the budget are also studied, and it is found that the temporal and spatial resolution of the SESAME regional network is marginal for diagnosing convective effects on a horizontal time scale of 550 x 550 km.

Kuo, Y.-H.↗

Mesoscale budgets of heat and moisture in a convective system over the central United States

Mesoscale heat and moisture budget calculations from the April 10-11 AVE-SESAME central U.S. region are calculated in order to diagnose the effect of midlatitude organized convection on its environment. When averaged over an area greater than the observational scale, the noise levels of 5 C/day for the heat budget and 2 g/kg per day for the moisture budget are considerably reduced. The credibility of such area-averaged budget results is indicated by the general agreement obtained between the observed rainfall rate and the vertically integrated heat sources and moisture sinks. The vertical convective heating that is diagnosed from this organized midlatitude convection differs significantly from tropical structures diagnosed on much larger temporal and spatial scales. A time lag of several hours between the moisture convergence and rainfall rate is noted.

Kuo, Y.-H.↗

Budgets of divergent and rotational kinetic energy during two periods of intense convection

The derivations of the energy budget equations for divergent and rotational components of kinetic energy are provided. The intense convection periods studied are: (1) synoptic scale data of 3 or 6 hour intervals and (2) mesoalphascale data every 3 hours. Composite energies and averaged budgets for the periods are presented; the effects of random data errors on derived energy parameters is investigated. The divergent kinetic energy and rotational kinetic energy budgets are compared; good correlation of the data is observed. The kinetic energies and budget terms increase with convective development; however, the conversion of the divergent and rotational energies are opposite.

Buechler, D. E.↗

Budget availability

A forecast of the total NASA budget required to achieve a manned mission to Mars at around the end of this century is described. A methodology is presented for projecting the major components of the NASA budget, including the NASA base, space flight, space station, Shuttle Derived Launch Vehicle, and the Manned Mars Mission. The NASA base, including administrative expenses, construction of facilities and research and development other than manned flight, is assumed to level off at the present (1985) level and remain constant at approximately $3.5 billion (constant fiscal year 1985 dollars). The budget for space flight, which consists of Shuttle research and development, operations, and tracking and data acquisition costs, is projected to decrease from approximately $4 billion in 1985 to just under $2.5 billion by 1989 and then level off. Planning profiles for three major programs are constructed: a permanently manned space station; a Shuttle Derived Vehicle; and a Manned Mars Mission. It is concluded that all of the programs can be conducted by the year 2002 with a 3 percent real growth rate in the NASA budget.

Cyr, Kelley J.↗

Reynolds-stress and dissipation rate budgets in a turbulent channel flow

The budgets for the Reynolds stresses and for the dissipation rate of the turbulence kinetic energy are computed using direct simulation data of a turbulent channel flow. The budget data reveal that all the terms in the budget become important close to the wall. For inhomogeneous pressure boundary conditions, the pressure-strain term is split into a return term, a rapid term, and a Stokes term. The Stokes term is important close to the wall. The rapid and return terms play different roles depending on the component of the term. A split of the velocity pressure-gradient term into a redistributive term and a diffusion term is proposed, which should be simpler to model. The budget data is used to test existing closure models for the pressure-strain term, the dissipation rate, and the transport rate. In general, further work is needed to improve the models.

Mansour, N. N.↗

Reynolds-stress and dissipation-rate budgets in a turbulent channel flow

The budgets for the Reynolds stresses and for the dissipation rate of the turbulence kinetic energy are computed using direct simulation data of a turbulent channel flow. The budget data reveal that all the terms in the budget become important close to the wall. For inhomogeneous pressure boundary conditions, the pressure-strain term is split into a return term, a rapid term, and a Stokes term. The Stokes term is important close to the wall. The rapid and return terms play different roles depending on the component of the term. A split of the velocity pressure-gradient term into a redistributive term and a diffusion term is proposed, which should be simpler to model. The budget data is used to test existing closure models for the pressure-strain term, the dissipation rate, and the transport rate. In general, further work is needed to improve the models.

Mansour, N. N.↗