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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 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1993

Runtime support and compilation methods for user-specified data distributions

This paper describes two new ideas by which an HPF compiler can deal with irregular computations effectively. The first mechanism invokes a user specified mapping procedure via a set of compiler directives. The directives allow use of program arrays to describe graph connectivity, spatial location of array elements, and computational load. The second mechanism is a simple conservative method that in many cases enables a compiler to recognize that it is possible to reuse previously computed information from inspectors (e.g. communication schedules, loop iteration partitions, information that associates off-processor data copies with on-processor buffer locations). We present performance results for these mechanisms from a Fortran 90D compiler implementation.

Ponnusamy, Ravi↗
NASA NTRS1991

Growth-speed dependence of primary arm spacings in directionally solidified Pb-10 wt pct Sn

The dependence of primary arm spacings on growth speed has been investigated for cellular and dendritic arrays in directionally solidified Pb-10 wt pct Sn. The spatial arrangements of cells and dendrites, as given by their coordination number, are not very different from each other. The primary arm spacing maxima and the cell-to-dendrite transition appear to be strongly influenced by the magnitude of the solute partition coefficient (k). The planar-to-cellular transition in Pb-Sn (k = 0.50) is supercritical as compared to the subcritical behavior reported in Al-Cu (k = 0.14) and succinonitrile-acetone (k = 0.1).

Chopra, M. A.↗
NASA NTRS2013

An Extension of the Time-Spectral Method to Overset Solvers

Relative motion in the Cartesian or overset framework causes certain spatial nodes to move in and out of the physical domain as they are dynamically blanked by moving solid bodies. This poses a problem for the conventional Time-Spectral approach, which expands the solution at every spatial node into a Fourier series spanning the period of motion. The proposed extension to the Time-Spectral method treats unblanked nodes in the conventional manner but expands the solution at dynamically blanked nodes in a basis of barycentric rational polynomials spanning partitions of contiguously defined temporal intervals. Rational polynomials avoid Runge's phenomenon on the equidistant time samples of these sub-periodic intervals. Fourier- and rational polynomial-based differentiation operators are used in tandem to provide a consistent hybrid Time-Spectral overset scheme capable of handling relative motion. The hybrid scheme is tested with a linear model problem and implemented within NASA's OVERFLOW Reynolds-averaged Navier- Stokes (RANS) solver. The hybrid Time-Spectral solver is then applied to inviscid and turbulent RANS cases of plunging and pitching airfoils and compared to time-accurate and experimental data. A limiter was applied in the turbulent case to avoid undershoots in the undamped turbulent eddy viscosity while maintaining accuracy. The hybrid scheme matches the performance of the conventional Time-Spectral method and converges to the time-accurate results with increased temporal resolution.

Leffell, Joshua Isaac↗
DOE OSTI2023

Ecohydrological decoupling under changing disturbances and climate

Terrestrial disturbances are increasing in frequency and severity, perturbing the hydrologic cycle by altering vegetation-mediated water use and microclimate. Changes in the hydrological cycle alter vegetation succession, which is additionally influenced by changing climate and atmospheric CO 2 . Here, the interacting drivers and feedbacks between disturbances, climate, and vegetation cause uncertainty regarding the sustainable provision of freshwater through streamflow. Here we synthesize the literature on post-disturbance ecohydrological coupling, in particular, including the mechanistic relationship between vegetation and streamflow, under changing disturbance regimes, atmospheric CO 2 , and climate. Disturbance can cause decoupling between transpiration and streamflow by altering the connectivity, size, availability, and spatial distribution of their source pools. Decoupling increases when soil moisture is low due to reduced connectivity, and when soil moisture is high and Q and T are independent. Successional trajectories regulate the physiological and physical features influencing influence the dynamics of source water partitioning. Changing climate and disturbance regimes can alter succession and prolong decoupling, with potential moderation by CO 2 . Increasing rates, severity, and spread of disturbances along with warming could promote greater decoupling globally. From this review emerges a framework of testable hypotheses that identify the critical processes regulating ecohydrological coupling and provides a roadmap for future research. Accurate prediction of post-disturbance coupling and subsequent water availability for human consumption requires understanding the degree of hydraulic connectivity between source water pools for transpiration and streamflow and their response to succession under changing disturbance and climate regimes.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2006

Effects of data selection on the assimilation of AIRS data

The Atmospheric InfraRed Sounder (AIRS), flying aboard NASA's Earth Observing System (EOS) Aqua satellite with the Advanced Microwave Sounding Unit-A (AMSU-A), has been providing data for use in numerical weather prediction (NWP) and data assimilation systems (DAS) for over three years. The full AIRS data set is currently not transmitted in near-real-time (NRT) to the NWP centers. Instead, data sets with reduced spatial and spectral information are produced and made available in NRT. In this paper, we evaluate the use of different channel selections and error specifications. We achieved significant positive impact from the Aqua AIRS/AMSU-A combination in both hemispheres during our experimental time period of January 2003. The best results were obtained using a set of 156 channels that did not include any in the 6.7micron water vapor band. The latter have a large influence on both temperature and humidity analyses. If observation and background errors are not properly specified, the partitioning of temperature and humidity information from these channels will not be correct, and this can lead to a degradation in forecast skill. We found that changing the specified channel errors had a significant effect on the amount of data that entered into the analysis as a result of quality control thresholds that are related to the errors. However, changing the channel errors within a relatively small window did not significantly impact forecast skill with the 155 channel set. We also examined the effects of different types of spatial data reduction on assimilated data sets and NWP forecast skill. Whether we picked the center or the warmest AIRS pixel in a 3x3 array affected the amount of data ingested by the analysis but had a negligible impact on the forecast skill.

Joiner, Joanna↗
DOE OSTI2023

Refined views of ancient ocean chemistry: Tracking trace element incorporation in pyrite framboids using atom probe tomography

The trace element chemistry of pyrite can be used to determine the origin, timing, and conditions of formation of ore deposits; as a vectoring tool for mineral exploration; and to determine the evolution of the Earth’s oceanic and atmospheric chemistry. However, little is known about whether trace elements are held with the pyrite structure or within nano-inclusions of other phases. This distinction is important for two primary reasons. First, trace element incorporation into the pyrite structure can affect the partitioning of other trace elements. Second, if trace elements are held within nano-inclusions, the partition coefficient of the mineral phases that make up the nano-inclusion, rather than pyrite, are the critical consideration in related interpretations. Previous studies addressing this topic have used laser ablation inductively coupled plasma mass spectrometry; however, the resulting data do not provide sufficient spatial resolution to delineate trace element distributions unless the inclusions are large. Further, they use these flat element profiles in time resolved laser ablation output graphs to argue that pyrite trace element content provides a direct relationship between trace element content of seawater and pyrite trace element content. To improve resolution, we have used atom probe tomography to characterize trace element distributions in pyrite framboids from the Cariaco Basin and Demerara Rise in three-dimensions at sub-nanometer resolution. Manganese was found to be concentrated in the pyrite nanocrystal part of the original framboid structure. In contrast, Ni was mostly found along the grain boundary, though it still appeared to be contained within the pyrite structure. Copper was concentrated in later pyrite overgrowths, and As varied in its location. These observations suggest that some important trace elements are incorporated into pyrite during early diagenesis, even in euxinic settings dominated by water-column pyrite formation. Statistical analysis was used to determine whether trace elements were incorporated in the lattice or within nanoscale inclusions (referred to here are nano-inclusions). We found that As, Ni, Cu, and Mn were commonly held within the pyrite structure, but As, Ni, and Cu can also be held as nano-inclusions or within grain interfaces. Incorporation of As is known to enhance the incorporation of other trace elements and in this case appears to correlated to elevated Ni and Cu concentrations in the Cariaco Basin samples. Furthermore, understanding these relationships strongly impacts our ability to utilize pyrite trace metal concentrations to analyze and quantify early ocean chemistry and its evolution through time.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Real-Time Measurements of Gas-Phase Medium-Chain Chlorinated Paraffins Reveal Daily Changes in Gas-Particle Partitioning Controlled by Ambient Temperature

Chlorinated paraffins (CPs) are synthetic polychlorinated n-alkanes produced as mixtures of a range of C x Cl y H 2x–y+2 formulas. CPs have numerous industrial applications but are toxic, long-lived, and environmentally ubiquitous with environmental releases occurring throughout their production, use, and disposal. Short-chain chlorinated paraffins (SCCPs, C 10–13 ) have been regulated by the United States Environmental Protection Agency since 2009 and by the Stockholm Convention since 2017. SCCP regulation is expected to cause increased production of medium-chain chlorinated paraffins (MCCPs; C 14–17 ), which are currently under consideration for Stockholm Convention regulations. Thus, there is a need to improve the understanding of MCCP environmental transport, distribution, and fate. Existing measurements are limited in their spatial and temporal coverage. Measurements of CP atmospheric loading are particularly scarce. Historically, these measurements have required long sampling times, obscuring the temporal behavior of atmospheric CPs. We report real-time in situ measurements of 18 gas-phase MCCPs. These measurements were made in the United States Southern Great Plains with nitrate ion chemical ionization mass spectrometry (NO 3 –CIMS). Here, the estimated average lower-limit concentration of MCCPs is on the order of single-digit ng/m 3 . MCCP diel behavior is partially explained by gas-particle partitioning with implications for MCCP transport and lifetimes.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Spectral deferred correction methods for high-order accuracy in poroelastic problems

In this work, we investigate high-order accuracy in time integration by examining two operator splitting methods for poroelastic problems: the two-pass and the spectral deferred correction (SDC) methods. To enhance the order of accuracy, the two-pass method partitions a coupled operator symmetrically, whereas the SDC method corrects truncation errors by establishing an error equation. These high-order methods are applied to underlying solution strategies, i.e., monolithic, fixed-stress sequential, and undrained sequential methods. We observe that semi-discretized systems from spatial discretization have forms similar to those of index-1 differential algebraic equations (DAEs), causing order reduction against the two-pass method when it is used in conjunction with either the monolithic or sequential method. On the other hand, the SDC in conjunction with the monolithic method exhibits the desired second-order accuracy in poroelastic problems while increasing the order of accuracy for index-1 DAEs. However, the SDC in conjunction with either of the two sequential methods does not achieve the desired order of accuracy, and maintains first order because the flow equation for poroelasticity has an additional approximation associated with the volumetric strain rate term, which does not yield exactly the same forms as those of conventional DAEs. Thus, the monolithic SDC method can achieve higher-order accuracy, but may require higher computational costs because it involves solving matrix systems larger than those for the sequential methods.

02 PETROLEUM↗
DOE OSTI2023

Using Direct Laboratory Measurements of Electron Temperature Anisotropy to Identify the Heating Mechanism in Electron-Only Guide Field Magnetic Reconnection

Anisotropic electron heating during electron-only magnetic reconnection with a large guide magnetic field is directly measured in a laboratory plasma through in situ measurements of electron velocity distribution functions. Electron heating preferentially parallel to the magnetic field is localized to one separatrix, and anisotropies of 1.5 are measured. The mechanism for electron energization is identified as the parallel reconnection electric field because of the anisotropic nature of the heating and spatial localization. These characteristics are reproduced in a 2D particle-in-cell simulation and are also consistent with numerous magnetosheath observations. A measured increase in the perpendicular temperature along both separatrices is not reproduced by our 2D simulations. Here, this work has implications for energy partition studies in magnetosheath and laboratory reconnection.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
NASA NTRS2000

Aspects of Boreal Forest Hydrology: From Stand to Watershed

This report evaluates land surface hydrologic processes in the boreal forest using observations collected during the Boreal Ecosystem Atmospheric Study (BOREAS), carried out in the boreal forest of central Canada from 1994 to 1996. Three separate studies, each of which constitutes a journal publication, are included. The first study describes the application of a spatially-distributed hydrologic model, originally developed for mid-latitude forested environments, to selected BOREAS flux measurement sites. Compared to point observations at the flux towers, the model represented energy and moisture fluxes reasonably well, but shortcomings were identified in the soil thermal submodel and the partitioning of evapotranspiration into canopy and subcanopy components. As a first step towards improving this partitioning, the second study develops a new parameterization for transmission of shortwave radiation through boreal forest canopies. The new model accounts for the transmission of diffuse and direct shortwave radiation and accounts for multiple scattering in the canopy and multiple reflections between the canopy layers.

Nijssen, B.↗
NASA NTRSDate not supplied

Data Fusion and Mining Techniques to Map Water Use and Drought across Spatial and Temporal Scales

As the world’s water resources come under increasing tension due to dual stressors of climate change and population growth, accurate knowledge of water consumption through evapotranspiration (ET) over a range in spatial scales will be critical in developing adaptation strategies. Remote sensing methods for monitoring consumptive water use (e.g, ET) are becoming increasingly important, especially in areas of significant water and food insecurity. One method to estimate ET from satellite-based methods, the Atmosphere Land Exchange Inverse (ALEXI) model uses the change in mid-morning land surface temperature to estimate the partitioning of sensible and latent heat fluxes which are then used to estimate daily ET. This presentation will outline several recent enhancements to the ALEXI modeling system, with a focus on global ET and drought monitoring. Until recently, ALEXI has been limited to areas with high resolution temporal sampling of geostationary sensors. The use of geostationary sensors makes global mapping a complicated process, especially for real-time applications, as data from as many as five different sensors are required to be ingested and harmonized to create a global mosaic. However, our research team has developed a new and novel method of using twice-daily observations from polar-orbiting sensors such as MODIS and VIIRS to estimate the mid-morning rise in LST that is used to drive the energy balance estimations within ALEXI. This allows the method to be applied globally using a single sensor (in this case, initially MODIS with a planned transition to VIIRS) rather than a global compositing of all available geostationary data. Other advantages of this new method include the higher spatial resolution provided by MODIS and VIIRS and the increased sampling at high latitudes where oblique view angles limit the utility of geostationary sensors. This presentation will focus on global applications for mapping water use and drought using data mining and data fusion across spatial scales extending from 5-km to 30-m “field-scale” estimates.

Christopher Hain↗
DOE OSTI2021

Real-time streamflow forecasting: AI vs. Hydrologic insights

In this paper, we propose a set of simple benchmarks for the evaluation of data-based models for real-time streamflow forecasting, such as those developed with sophisticated Artificial Intelligence (AI) algorithms. The benchmarks are also data-based and provide context to judge incremental improvements in the performance metrics from the more complicated approaches. The benchmarks include temporal and spatial persistence, persistence corrected for baseflow and streamflow, as well as river distance weighted runoff obtained from space-time distributed rainfall. In the development of the benchmarks, we use basic hydrologic insights such as flow aggregation by the river network, scale-dependence in basin response, streamflow partitioning into quick flow and baseflow, water travel time, and rainfall averaging by the basin width function. The study uses 140 streamflow gauges in Iowa that cover a range of basin scales between 7 and 37,000 km 2 . The data cover 17 years. This work demonstrates that the proposed benchmarks can provide good performance according to several commonly used metrics. For example, streamflow forecasting at half of the test locations across years achieves a Kling-Gupta Efficiency (KGE) score of 0.6 or higher at one-day ahead lead time, and 20% of cases reach the KGE of 0.8 or higher. The proposed benchmarks are easy to implement and should prove useful for developers of data-based as well as physics-based hydrologic models and real-time data assimilation techniques.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2020

Regional patterns in hydrologic response, a new three-component metric for hydrograph analysis and implications for ecohydrology, Northwest Volcanic Aquifer Study Area, USA

Spatial patterns of hydrologic response were examined for the Northwest Volcanic Aquifer Study Area (NVASA). The utility of established hydrograph-separation methods for assessing hydrologic response in permeable volcanic terranes was assessed and a new three-component metric for hydrograph analysis was developed. The new metric, which partitions streamflow into subcomponents defined by the timescales of hydrologic response (e.g., fast-runoff, intermediate-interflow and slow-baseflow), was used to gain a fundamental understanding of the regional hydrology, investigate sub-regional differences, influencing factors, and ecohydrological implications. The combined effects of NVASA’s physiography, climate and geology create a strongly coupled surface-groundwater system that produces copious baseflow and limited quantities of runoff and interflow. Patterns of hydrologic response are influenced by the type and rate of precipitation and permeability of the underlying geology. Under variable precipitation conditions the hydrologic response of volcanic terranes with similar permeability and subsurface-storage capacity can be significantly different. From a water management and ecohydrology perspective, understanding regional patterns of hydrologic response and sub-regional differences is fundamental. Results indicate that minimum-flow methods provide the most conservative estimate of baseflow and may be the most robust for filtering out snowmelt bias in baseflow estimates. Baseflow contributes ~75% of the perennial streamflow across the NVASA and represents a critical component of the regional water supply that provides critical cold-water habitat.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

The ABCflux database: Arctic–boreal CO 2 flux observations and ancillary information aggregated to monthly time steps across terrestrial ecosystems

Past efforts to synthesize and quantify the magnitude and change in carbon dioxide (CO 2 ) fluxes in terrestrial ecosystems across the rapidly warming Arctic–boreal zone (ABZ) have provided valuable information but were limited in their geographical and temporal coverage. Furthermore, these efforts have been based on data aggregated over varying time periods, often with only minimal site ancillary data, thus limiting their potential to be used in large-scale carbon budget assessments. To bridge these gaps, we developed a standardized monthly database of Arctic–boreal CO 2 fluxes (ABCflux) that aggregates in situ measurements of terrestrial net ecosystem CO 2 exchange and its derived partitioned component fluxes: gross primary productivity and ecosystem respiration. The data span from 1989 to 2020 with over 70 supporting variables that describe key site conditions (e.g., vegetation and disturbance type), micrometeorological and environmental measurements (e.g., air and soil temperatures), and flux measurement techniques. Here, we describe these variables, the spatial and temporal distribution of observations, the main strengths and limitations of the database, and the potential research opportunities it enables. In total, ABCflux includes 244 sites and 6309 monthly observations; 136 sites and 2217 monthly observations represent tundra, and 108 sites and 4092 observations represent the boreal biome. The database includes fluxes estimated with chamber (19 % of the monthly observations), snow diffusion (3 %) and eddy covariance (78 %) techniques. The largest number of observations were collected during the climatological summer (June–August; 32 %), and fewer observations were available for autumn (September–October; 25 %), winter (December–February; 18 %), and spring (March–May; 25 %). ABCflux can be used in a wide array of empirical, remote sensing and modeling studies to improve understanding of the regional and temporal variability in CO 2 fluxes and to better estimate the terrestrial ABZ CO 2 budget.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Facile alignment estimation in carbon nanotube films using image processing

Whether a macroscopic assembly of carbon nanotubes can exhibit the one-dimensional properties expected from individual nanotubes critically depends on how well the nanotubes are aligned inside the assembly. Therefore, a simple and accurate method for assessing the degree of alignment is desired for the rapid characterization of carbon nanotube films and fibers. Here, we present an end-to-end solution for determining the global and local spatial orientation of carbon nanotubes in films within a short amount of time using a fast, precise, and economical approach based on an image processing method applied to scanning electron microscopy images. Further, we first use Laplacian edge enhancement filtering for improving the appearance of edge regions, which is followed by image partitioning into multiple blocks to capture the nanoscale orientation characteristics and total variation-based image decomposition of these image blocks. We then perform a 2D-fast Fourier transform on the image decomposed textural components of these edge-enhanced image blocks to determine the orientation distribution, which is utilized to estimate the 2D nematic order parameter. To show the effectiveness of our method, we corroborated our results against results obtained with other state-of-the-art image processing and experimental techniques.

2D-FFT↗
NASA NTRS1998

Nitrogen Species in the Post-Pinatubo Stratosphere: Model Analysis Utilizing UARS Measurements

We present an analysis of the impact of heterogeneous chemistry on the partitioning of nitrogen species measured by the Upper Atmosphere Research Satellite (UARS) instruments. The UARS measurements utilized include: N2O, HNO3 and ClONO2 (Cryogen Limb Array Etalon Spectrometer (CLAES), version 7), temperature, methane, ozone, H2O, HCl, NO and NO2 (HALogen Occultation Experiment (HALOE), version 18). The analysis is carried out for the data from January 1992 to September 1994 in the 100-1 mbar (approx.17-47 km) altitude range and over 10 degree latitude bins from 70degS to 70degN. Temporal-spatial evolution of aerosol surface area density (SAD) is adopted according to the Stratospheric Aerosol and Gas Experiment (SAGE) 11 data. A diurnal steady-state photochemical box model, constrained by the temperature, ozone, H2O, CH4, aerosol SAD and columns of O2 and O3 above the point of interest, has been used as the main tool to analyze these data. Total inorganic nitrogen (NO(y)) is obtained by three different methods: (1) as a sum of the UARS measured NO, NO2, HNO3, and ClONO2; (2) from the N2O-NO(y) correlation, and (3) from the CH4-NO(y) correlation. To validate our current understanding of stratospheric heterogeneous chemistry for post-Pinatubo conditions, the model-calculated NO(x)/NO(y) ratios and the NO, NO2, and HNO3 profiles are compared to the UARS-derived data. In general, the UARS-constrained box model captures the main features of nitrogen species partitioning in the post-Pinatubo years. However, the model underestimates the NO2 content, particularly, in the 30-7 mbar (approx. 23-32 km) range. Comparisons of the calculated temporal behavior of the partial columns of NO2 and HNO3 and ground based measurements at 45degS and 45degN are also presented. Our analysis indicates that ground-based and HALOE v. 18 measurements of the NO2 vertical columns are consistent within the range of their uncertainties and are systematically higher (up to 50%) than the model results at mid-latitudes in both hemispheres. Reasonable agreement is obtained for HNO3 columns at 45degS suggesting some problems with nitrogen species partitioning in the model. Outstanding uncertainties are discussed.

Danilin, M. Y.↗
DOE OSTI2020

Lipid sponge droplets as programmable synthetic organelles

Living cells segregate molecules and reactions in various subcellular compartments known as organelles. Spatial organization is likely essential for expanding the biochemical functions of synthetic reaction systems, including artificial cells. Many studies have attempted to mimic organelle functions using lamellar membrane-bound vesicles. However, vesicles typically suffer from highly limited transport across the membranes and an inability to mimic the dense membrane networks typically found in organelles such as the endoplasmic reticulum. Here, we describe programmable synthetic organelles based on highly stable nonlamellar sponge phase droplets that spontaneously assemble from a single-chain galactolipid and nonionic detergents. Due to their nanoporous structure, lipid sponge droplets readily exchange materials with the surrounding environment. In addition, the sponge phase contains a dense network of lipid bilayers and nanometric aqueous channels, which allows different classes of molecules to partition based on their size, polarity, and specific binding motifs. The sequestration of biologically relevant macromolecules can be programmed by the addition of suitably functionalized amphiphiles to the droplets. We demonstrate that droplets can harbor functional soluble and transmembrane proteins, allowing for the colocalization and concentration of enzymes and substrates to enhance reaction rates. Droplets protect bound proteins from proteases, and these interactions can be engineered to be reversible and optically controlled. Our results show that lipid sponge droplets permit the facile integration of membrane-rich environments and self-assembling spatial organization with biochemical reaction systems.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1996

Turbulence Scales, Rise Times, Caustics, and the Simulation of Sonic Boom Propagation

The general topic of atmospheric turbulence effects on sonic boom propagation is addressed with especial emphasis on taking proper and efficient account of the contributions of the portion oi the turbulence that is associated with extremely high wavenumber components. The recent work reported by Bart Lipkens in his doctoral thesis is reexamined to determine whether the good agreement between his measured rise times with the 1971 theory of the author is fortuitous. It is argued that Lipken's estimate of the distance to the first caustic was a gross overestimate because of the use of a sound speed correlation function shaped like a gaussian curve. In particular, it is argued that the expected distance to the first caustic varies with the kinematic viscosity nu and the energy epsilon dissipated per unit mass per unit time, and the sound speed c as : d(sub first caustic) = nu(exp 7/12) c(exp 2/3)/ epsilon(exp 5/12)(nu x epsilon/c(exp 4))(exp a), where the exponent a is greater than -7/12 and can be argued to be either O or 1/24. In any event, the surprising aspect of the relationship is that it actually goes to zero as the viscosity goes to zero with s held constant. It is argued that the apparent overabundance of caustics can be grossly reduced by a general computational and analytical perspective that partitions the turbulence into two parts, divided by a wavenumber k(sub c). Wavenumbers higher than kc correspond to small-scale turbulence, and the associated turbulence can be taken into account by a renormalization of the ambient sound speed so that the result has a small frequency dependence that results from a spatial averaging over of the smaller-scale turbulent fluctuations. Selection of k(sub c). can be made so large that only a very small number of caustics are encountered if one adopts the premise that the frequency dispersion of pulses is caused by that part of the turbulence spectrum which lies in the inertial range originally predicted by Kolmogoroff. The acoustic propagating wave's dispersion relation has the acoustic wavenumber being of the form k = (omega/c) + F(omega), where c is a spatially averaged sound speed and where, for mechanical turbulence, the extra term F(omega) must depend on only the angular frequency omega, the sound speed c, and the turbulent energy dissipation epsilon per unit fluid mass and per unit time. If the turbulence is weak, then the quantity F(omega) has to be of second order in the portions of the turbulent fluid velocity in the inertial range, so, following Kolmogoroff's reasoning, it must vary with epsilon as epsilon(exp 2/3). Simple dimensional analysis then reveals that F(omega) is K epsilon(exp 2/3) c(exp -7/3) omega(exp l/3), K being a universal dimensionless complex constant.

Pierce, Allan D.↗