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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Performance assessment of long-legged tightly-baffled divertor geometries in the ARC reactor concept

Extremely intense power exhaust channels are projected for tokamak-based fusion power reactors; a means to handle them remains to be demonstrated. Advanced divertor configurations have been proposed as potential solutions. Recent modelling of tightly baffled, long-legged divertor geometries for the divertor test tokamak concept, ADX, has shown that these concepts may access passively stable, fully detached regimes over a broad range of parameters. The question remains as to how such divertors may perform in a reactor setting. To explore this, numerical simulations are performed with UEDGE for the long-legged divertor geometry proposed for the ARC pilot plant conceptual design - a device with projected heat flux power width (λq||) of 0.4 mm and power exhaust of 93 MW - first for a simplified Super-X divertor configuration (SXD) and then for the actual X-point target divertor (XPTD) being proposed. It is found that the SXD, combined with 0.5% fixed-fraction neon impurity concentration, can produce passively stable, detached divertor regimes for power exhausts in the range of 80-108 MW - fully accommodating ARC's power exhaust. The XPTD configuration is found to reduce the strike-point temperature by a factor of ~10 compared to the SXD for small separations (~1.4λq||) between main and divertor X-point magnetic flux surfaces. Even greater potential reductions are identified for reducing separations to ~1λq|| or less. The power handling response is found to be insensitive to the level of cross-field convective or diffusive transport assumed in the divertor leg. By raising the separatrix density by a factor of 1.5, stable fully detached divertor solutions are obtained that fully accommodate the ARC exhaust power without impurity seeding. To our knowledge, this is the first time an impurity-free divertor power handling scenario has been obtained in edge modelling for a tokamak fusion power reactor with λq|| of 0.4 mm.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Pushing the limits of size selectivity in nanoscale solute separations

Transport of a spherical solute through a cylindrical pore has been modelled for decades using well-established hindered transport theory, predicting solutes with a size smaller than the pore to be rejected nonetheless because of convective and diffusive hindrance; this rejection mechanism prevents extremely sharp solute separations by a membrane. Whereas the model has been historically verified, solute transport through near-perfect isoporous membranes may finally overcome this limitation. Here, in this study, encouraging solute rejections are achieved using nanofabricated, defect-free silicon nitride isoporous membranes. The membrane is challenged by a recirculated feed to increase the opportunity for interactions between solutes and the pore array. Results show the membrane completely reject solutes with greater size than the pore size while effectively allowing smaller solutes to permeate through. With effectively increasing the number of interactions, we propose that a steeper size-selective rejection curve may be achieved. With this traditional hurdle overcome, there is new promise for unprecedented membrane separations through judicious process design and extremely tight pore-size distributions.

Gao, Feng↗
DOE OSTI2023

Effects of Lower Troposphere Vertical Mixing on Simulated Clouds and Precipitation Over the Amazon During the Wet Season

Planetary boundary layer (PBL) schemes parameterize unresolved turbulent mixing within the PBL and free troposphere (FT). Previous studies reported that precipitation simulation over the Amazon in South America is quite sensitive to PBL schemes and the exact relationship between the turbulent mixing and precipitation processes is, however, not disentangled. In this study, regional climate simulations over the Amazon in January–February 2019 are examined at process level to understand the precipitation sensitivity to PBL scheme. The focus is on two PBL schemes, the Yonsei University (YSU) scheme, and the asymmetric convective model v2 (ACM2) scheme, which show the largest difference in the simulated precipitation. During daytime, while the FT clouds simulated by YSU dissipate, clouds simulated by ACM2 maintain because of enhanced moisture supply due to the enhanced vertical moisture relay transport process: (a) vertical mixing within PBL transports surface moisture to the PBL top, and (b) FT mixing feeds the moisture into the FT cloud deck. Due to the thick cloud deck over Amazon simulated by ACM2, surface radiative heating is reduced and consequently the convective available potential energy is reduced. As a result, precipitation is weaker from ACM2. Two key parameters dictating the vertical mixing are identified, p , an exponent determining boundary layer mixing and λ , a scale dictating FT mixing. Sensitivity simulations with altered p , λ , and other treatments within YSU and ACM2 confirm the precipitation sensitivity. The FT mixing in the presence of clouds appears most critical to explain the sensitivity between YSU and ACM2.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

A large-eddy simulation exploration of the assumptions used in retrieving entrainment from a mixing diagram approach with ground-based remote sensors

Entrainment is a crucial component of the atmospheric boundary layer (BL) moisture and heat budget. While usually thought of as only entrainment flux, entrainment within the mixed layer budget equation is really composed of two terms: the flux of a property across the boundary separating the BL from the free troposphere and the change in the concentration of a property as the depth of the BL changes. In a recent study, Wakefield et al. (2023) used ground-based remote-sensing observations to estimate entrainment flux as the residual of a mixing diagram framework that was applied to the daytime convective boundary layer. This present work uses large-eddy simulation (LES) to examine how well this residual assumption for entrainment fluxes alone compares to the actual sum of those two entrainment terms derived from spatial averages of the LES output. We highlight the importance of the second entrainment term in closing the mixed layer budget and show that the residual assumption does not represent entrainment flux only but rather a total entrainment term when the boundary layer depth is changing.

Rosenberger, Tessa E. [Cleveland State Univ., Clev↗
DOE OSTI2020

Temporal dynamics of large-scale structures for turbulent Rayleigh–Bénard convection in a moderate aspect-ratio cylinder

We investigate the spatial organization and temporal dynamics of large-scale, coherent structures in turbulent Rayleigh–Bénard convection via direct numerical simulation of a 6.3 aspect-ratio cylinder with Rayleigh and Prandtl numbers of 9.6×10 7 and 6.7, respectively. Fourier modal decomposition is performed to investigate the structural organization of the coherent turbulent motions by analysing the length scales, time scales and the underlying dynamical processes that are ultimately responsible for the large-scale structure formation and evolution. We observe a high level of rotational symmetry in the large-scale structure in this study and that the structure is well described by the first four azimuthal Fourier modes. Two different large-scale organizations are observed during the duration of the simulation and these patterns are dominated spatially and energetically by azimuthal Fourier modes with frequencies of 2 and 3. Studies of the transition between these two large-scale patterns, radial and vertical variations in the azimuthal energy spectra, as well as the spatial and modal variations in the system's correlation time are conducted. Rotational dynamics are observed for individual Fourier modes and the global structure with strong similarities to the dynamics that have been reported for unit aspect-ratio domains in prior works. It is shown that the large-scale structures have very long correlation time scales, on the order of hundreds to thousands of free-fall time units, and that they are the primary source for a horizontal inhomogeneity within the system that can be observed during a finite, but a very long-time simulation or experiment.

42 ENGINEERING↗
DOE OSTI2023

Description and Evaluation of a New Deep Convective Cloud Model Considering In-cloud Inhomogeneity

Convections still need to be parameterized in general circulation models (GCMs) in the coming decades. Performances of GCMs are significantly influenced by the convection schemes used. In contrast to most conventional cloud models that ignore in-cloud inhomogeneities, a new convective cloud model explicitly considering in-cloud inhomogeneities is developed. The new model adopts a single bulk plume approach, but divides the plume into a series of interacting sub-plumes in order to mimic the transition from the plume core to its edges. We implemented the new cloud model in NCAR Community Atmosphere Model version 5.0 (CAM5) and evaluated its performance. Single-column tests show a stronger mass flux profile and low-level detrainment with the new model. In global simulations, the long-lasting wet bias in the tropical free troposphere of CAM5 is alleviated. Spatial pattern and intensity distribution of precipitation is improved, but the global hydrological cycle is slightly over-enhanced. The diurnal cycle of tropical precipitation is also better captured though the precipitation peak still occurs earlier than the observations and the amplitude of the cycle tends to weaken. MJO simulation is slightly improved with the new scheme. In addition, the new cloud model generated more tropical cyclones, in better agreement with observations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Convective Momentum Transport and Its Impact on the Madden‐Julian Oscillation in E3SM‐MMF

Abstract Convective momentum transport (CMT) is the process of vertical redistribution of horizontal momentum by small‐scale turbulent flows from moist convection. Traditional general circulation models (GCMs) and their multiscale modeling framework (MMF) versions poorly represent CMT due to insufficient information of subgrid‐scale flows at each GCM grid. Here the explicit scalar momentum transport (ESMT) scheme for representing CMT is implemented in the Energy Exascale Earth System Model‐Multiscale Modeling Framework (E3SM‐MMF) with embedded 2‐D cloud‐resolving models (CRMs), and verified against E3SM‐MMF simulations with 3‐D CRMs and observations. The results show that representing CMT by ESMT helps reduce climatological mean precipitation model bias over the western Pacific and the ITCZ regions, which is attributed to the weakened mean easterlies over the Pacific. Also, CMT from simulations with 2‐D and 3‐D CRMs impose a similar impact on Kelvin waves by reducing their variability and slowing down their phase speed, but opposite impacts on the Madden‐Julian Oscillation (MJO) variability. The ESMT scheme readily captures the climatological mean spatial patterns of the zonal and meridional components of CMT and their variability across multiple time scales, but shows some differences in estimating its magnitude. CMT mainly affects the MJO by decelerating its winds in the free troposphere, but accelerates its near‐surface winds. This study serves as a prototype for implementing CMT scheme in the MMF simulations, highlighting its crucial role in reducing model bias in mean state and spatiotemporal variability.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Integral Kernel Methods for Nonlinear Parabolic-Elliptic Systems

Nonlinear parabolic-elliptic systems arise in many physical, biological, and chemical phenomena such as chemotaxis, ion transport, self-gravitating particles, and Brownian vortices. Existing methods struggle with the strong coupling and high nonlinearity and nonlocality of some of these systems, especially the ill-conditioned, convection-dominated problems. To overcome numerical difficulties, current approaches rely on initial guesses, preconditioning, or iterative techniques with no convergence guarantees. They might suffer from poor scalability, large memory usage, and difficulty to parallelize. Inspired by the connection of parabolic-elliptic systems to stochastic processes, we introduce a novel meshless, monolithic, and fully explicit method that naturally encapsulates the elliptic and parabolic operators into a single step which updates each node deterministically with global information. By being fully quadrature-based, it avoids solving systems of discretized equations and does not utilize initial guesses or preconditioning, while requiring little memory and being easy to parallelize. We first derive the method in an integral kernel formulation with quadratic complexity in the number of integration nodes and then leverage kernel-independent fast multipole methods (FMM) to present a scalable algorithm with linear complexity. We provide numerical examples for the Poisson-Nernst-Planck equations in one, two, and three dimensions, together with the derivation of the integral kernel for each case. Furthermore, the examples demonstrate the fast convergence and scalability of the FMM-accelerated algorithm, as well as its suitability for convection-dominated problems, making it competitive against traditional PDE solvers.

PDE systems↗
DOE OSTI2024

The Physics behind Precipitation Onset Bias in CMIP6 Models: The Pseudo-Entrainment Diagnostic and Trade-Offs between Lapse Rate and Humidity

Conditional instability and the buoyancy of plumes drive moist convection but have a variety of representations in model convective schemes. Vertical thermodynamic structure information from Atmospheric Radiation Measurement (ARM) sites and reanalysis (ERA5), satellite-derived precipitation (TRMM3b42), and diagnostics relevant for plume buoyancy are used to assess climate models. Previous work has shown that CMIP6 models represent moist convective processes more accurately than their CMIP5 counterparts. However, certain biases in convective onset remain pervasive among generations of CMIP modeling efforts. Here we diagnose these biases in a cohort of nine CMIP6 models with sub-daily output, assessing conditional instability in profiles of equivalent potential temperature θ e and saturation equivalent potential temperature θ es in comparison to a plume model with different mixing assumptions. Most models capture qualitative aspects of the θ es vertical structure, including a substantial decrease with height in the lower free troposphere associated with the entrainment of subsaturated air. We define a “pseudo-entrainment” diagnostic that combines subsaturation and a θ es measure of conditional instability similar to what entrainment would produce under the small-buoyancy approximation. This captures the trade-off between larger θ es lapse rates (entrainment of dry air) and small subsaturation (permits positive buoyancy despite high entrainment). This pseudo-entrainment diagnostic is also a reasonable indicator of the critical value of integrated buoyancy for precipitation onset. Models with poor θ e /θ es structure (those using variants of the Tiedtke Scheme) or low entrainment runs of CAM5, and models with low subsaturation, such as NASA-GISS, lie outside the observational range in this diagnostic.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

A dynamic thermal algal growth model for pilot-scale open-channel raceways

Here this study describes the makeup of and results from a simulation consisting of a lumped thermal model integrated with a dynamic algae growth model to simulate the microalgae productivity of an open-channel raceway cultivation system. The thermal model considers the dynamic effects of weather, light absorption, convective heat transfer, radiation heat transfer, conductive heat transfer, thermal capacitance, and water control strategies. The dynamic algae growth model solves a set of ordinary differential equations consisting of growth functions dependent on incident radiation, temperature, nutrient availability, basal metabolism, and losses due to dark- and photo-respiration. Relative errors in the predicted ash-free dry weight of Nannochloropsis oceanica are 12.5%, -6.1%, and 4.4% for three separate replicates of cultivation cycles (~4.2 m 2 ) performed at AzCATI during the ATP 3 Unified Field Studies in Fall, Spring, and Summer. This research demonstrates that thermal modeling is an essential contributor to the validation of microalgae growth models.

09 BIOMASS FUELS↗
DOE OSTI2024

Heterogeneous oxidation of hydrogen-natural gas blends in a safe, clean, and efficient burner design

The growth of hydrogen as an alternative clean fuel for fulfilling thermal energy needs of multiple economic sectors globally requires access to reliable, safe, energy efficient, emission free combustion technology. The work described in this short communication shows the applicability of a novel heterogeneous combustion design in utilizing a wide range of hydrogen blended methane concentrations to cleanly and safely generate thermal energy. The utilization of a simple first principles design approach along with engineered materials yielded a fuel-flexible hybrid infrared-convection burner design capable of lowering NOx emissions by more than 95% while simultaneously improving the heat transfer efficiency by 15% with a wide range of hydrogen concentrations. Here, the safety and performance of the combustion design was demonstrated in an burner at capacities of up to 12,000 Btu/h in producing temperatures of 900 °C. The atmospheric burner concept was integrated in a cooktop configuration with combined thermal power rating of 30,000 Btu/h and operated with hydrogen blended natural gas.

08 HYDROGEN↗
DOE OSTI2022

Aircraft Observations of Turbulence in Cloudy and Cloud-Free Boundary Layers Over the Western North Atlantic Ocean From ACTIVATE and Implications for the Earth System Model Evaluation and Development

This study examines boundary layer turbulence derived from high temporal resolution meteorological measurements from 40 research flights over the western North Atlantic Ocean during the 2020 deployments of ACTIVATE. Frequency distributions of various turbulent quantities reveal stronger turbulence during the winter deployment than in summer and for cloud‐topped than in cloud‐free boundary layers during the summer deployment. Maximum turbulence kinetic energy (TKE) is most often within cloud from observations in winter and summer, whereas it is mostly below cloud in both seasons by a global model turbulence parameterization. Further, bivariate frequency distributions are consistent with the bivariate Gaussian probability distribution functions assumed for the closure of higher‐order turbulence/shallow convection parameterizations used by some global models. Turbulence simulated by the Community Atmosphere Model version 6 and the Energy Exascale Earth System Model Atmosphere Model version 2 using such parameterizations is not as strong as observed, with more TKE going into vertical wind perturbations rather than into zonal wind perturbations as observed, suggesting that the treatment of turbulence in Earth system models still needs to be further improved.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

NPFTURBULENCE: Turbulent Parameters by airborne measurements

The original data were collected during the field campaign of “Turbulent layers promoting New Particle Formation” experiment (NPFTURBULENCE; https://www.arm.gov/research/campaigns/aaf2024npfturbulence) over the Atmospheric Radiation Measurement (ARM) user facility's Southern Great Plains (SGP) atmospheric observatory (https://www.arm.gov/capabilities/observatories/sgp ) in north-central Oklahoma. The ARM Aerial Facility ArcticShark uncrewed aerial system (UAS, https://www.arm.gov/capabilities/observatories/aaf/uas) was based at Blackwell–Tonkawa Municipal Airport (IATA: BWL, ICAO: KBKN, FAA LID: BKN, 36.74475° N, 97.34918° W, 313.9 m MSL), for the field campaign from May 5 through May 29, 2024. The ArcticShark UAS performed 11 flights, including 10 research flights over the Central Facility of the ARM SGP to measure atmospheric state, turbulence, surface IR temperature and imagery, and aerosol number concentration and size distribution. The current data set presents a comprehensive collection of turbulent parameters in the atmospheric boundary layer or lower free troposphere based on airborne measurement throughout the field campaign. The primary instruments used to create the current data set were the Aircraft Integrated Meteorological Measurement System (AIMMS-30) and the fine-wire thermocouple probe. For user convenience, the current data set includes several parameters commonly used in turbulent research for normalization and/or scaling: atmospheric boundary-layer height, surface conditions, convective scales for temperature, and velocity, etc.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Dynamic compression of water to conditions in ice giant interiors

Abstract Recent discoveries of water-rich Neptune-like exoplanets require a more detailed understanding of the phase diagram of H 2 O at pressure–temperature conditions relevant to their planetary interiors. The unusual non-dipolar magnetic fields of ice giant planets, produced by convecting liquid ionic water, are influenced by exotic high-pressure states of H 2 O—yet the structure of ice in this state is challenging to determine experimentally. Here we present X-ray diffraction evidence of a body-centered cubic (BCC) structured H 2 O ice at 200 GPa and ~ 5000 K, deemed ice XIX, using the X-ray Free Electron Laser of the Linac Coherent Light Source to probe the structure of the oxygen sub-lattice during dynamic compression. Although several cubic or orthorhombic structures have been predicted to be the stable structure at these conditions, we show this BCC ice phase is stable to multi-Mbar pressures and temperatures near the melt boundary. This suggests variable and increased electrical conductivity to greater depths in ice giant planets that may promote the generation of multipolar magnetic fields.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2020

Impact of Lateral Groundwater Flow and Subsurface Lower Boundary Conditions on Atmospheric Boundary Layer Development over Complex Terrain

Credible soil moisture redistribution schemes are essential to meteorological models, as lower boundary moisture influences the balance of surface turbulent fluxes and atmospheric boundary layer (ABL) development. While land surface models (LSMs) have vastly improved in their hydrologic representation, several commonly held assumptions, such as free-draining lower boundary, one-dimensional moisture flux, and lack of groundwater representation, can bias the terrestrial water balance. This study explores the impact of LSM hydrology representation on ABL development in the Weather Research and Forecasting (WRF) meteorological model. The results of summertime WRF simulations with Noah LSM, characterized by 2-m-thick soil and one-dimensional flow, are shown for a domain in the Colorado Rocky Mountain headwaters region. A reference WRF simulation is compared to 1) the same model with soil moisture initialized by the hydrologic model ParFlow; 2) a deep, free-draining simulation; and 3) WRF coupled to ParFlow, a three-dimensional, integrated groundwater-surface water model. Results show that both lateral transport of groundwater and the rate of drainage from the lower soil layer can weaken or reverse the coupling strength between evaporative fraction and ABL over a 5-month summer period. The resulting shifts in low-level moist convection in river valleys and thermally driven airflows yield strengthened anabatic upslope winds and perturbations to regional precipitation.

Forrester, Mary M.↗
DOE OSTI2021

Comparison of Observations and Predictions of Daytime Planetary-Boundary-Layer Heights and Surface Meteorological Variables in the Columbia River Gorge and Basin During the Second Wind Forecast Improvement Project

The second Wind Forecast Improvement Project (WFIP2) is an 18-month field campaign in the Pacific Northwest U.S.A., whose goal is to improve the accuracy of numerical-weather-prediction forecasts in complex terrain. The WFIP2 campaign involved the deployment of a large suite of in situ and remote sensing instrumentation, including eight 915-MHz wind-profiling radars, and surface meteorological stations. The evolution and annual variability of the daytime convective planetary-boundary-layer (PBL) height is investigated using the wind-profiling radars. Three models with different horizontal grid spacing are evaluated: the Rapid Refresh, the High-Resolution Rapid Refresh, and its nested version. The results are used to assess errors in the prediction of PBL height within the experimental and control versions of the models, with the experimental versions including changes and additions to the model parametrizations developed during the field campaign, and the control version using the parametrizations present in the National Oceanic and Atmospheric Administration/National Centers for Environmental Prediction operational version of the models at the start of the project. Results show that the high-resolution models outperform the low-resolution versions, the experimental versions perform better compared with the control versions, model PBL height estimations are more accurate on cloud-free days, and model estimates of the PBL height growth rate are more accurate than model estimates of the rate of decay. Finally, using surface sensors, we assess surface meteorological variables, finding improved surface irradiance and, to a lesser extent, improved 2-m temperature in the experimental version of the model.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Tropical Cyclone Wind Shear-Relative Asymmetry in Reanalyses

Abstract While tropical cyclones (TCs) are axisymmetric vortices to the first order, they often exhibit noteworthy structural asymmetries. These often result from environmental vertical wind shear, which tilts the vortex and induces a wavenumber 1 pattern in the circulation and precipitation fields. Reanalyses and climate models have improved in representing the TC structure and climatology, but their relatively coarse resolution and dependence on parameterized physics cast doubt on their ability to capture the asymmetric TC structure. We perform the most comprehensive process-oriented assessment of TC asymmetry to date in reanalyses. Specifically, we analyze the composite shear-relative TC structure in ERA5 and Climate Forecast System Reanalysis (CFSR), which vary in their resolutions, physical parameterization suites, and data assimilation techniques. These structures are compared with aircraft reconnaissance radar observations. In agreement with the observations, the strongest tangential winds are usually found left-of-shear, while inner core rainfall, ascent, vortex tilt, and low-level inflow are favored directly downshear or in the downshear-left quadrant. Outer rainband convection generally peaks in the downshear-right quadrant. Thermodynamic asymmetries are also apparent, with anomalous low-level moisture right-of-shear, midlevel warmth in the upshear-right quadrant (uptilt), and cloud properties suggestive of a realistic precipitation life cycle from growth to fallout. We also decompose rainfall contributions from the convective parameterization and large-scale cloud schemes and highlight the roles of vorticity advection, buoyancy advection, and diabatic processes in driving asymmetric vertical motions in the inner core and outer rainband regions. Our results suggest that process-level studies of TC asymmetry and TC–wind shear interaction under future warming are viable using climate models. Significance Statement Asymmetries are common in tropical cyclones (TCs), influencing their intensity, track, and hazards. Vertical wind shear often plays a leading-order role in causing these asymmetries. It is uncertain how well asymmetric structures and processes are captured in reanalyses and global climate models (GCMs) with grid spacings of 0.25° and coarser. In this study, we first evaluate TC asymmetry in reanalyses, which have the benefit of being forced by observations. This helps to assess whether the resolutions associated with GCMs sufficiently capture asymmetric structures and processes and motivates upcoming work with free-running GCMs to study how TC asymmetry may change in a warming climate.

Carstens, Jacob D.↗
DOE OSTI2020

Spatially resolved absolute densities of reactive species and positive ion flux in He-O 2 RF-driven atmospheric pressure plasma jet: touching and non-touching with dielectric substrate

Atmospheric pressure plasma jets (APPJs) are operating in direct contact with dielectric substrates for many applications. Nonetheless, many studies have been focusing on free jets. In this letter, we report spatially resolved measurements of reactive species including neutral and ionic species in an He + 1% O 2 RF-driven APPJ by molecular beam mass spectrometry equipped with a dielectric sampling plate, enabling to detect species densities for APPJ operating remotely or in direct contact with a substrate. Here, the spatially resolved distribution of O, O 2 (a 1 Δ g ) and O 3 is dominated by convection and, remarkably, shows minimum differences between touching and non-touching conditions.

74 ATOMIC AND MOLECULAR PHYSICS↗