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At least 253 records · Page 14

Increase in Levels of Stratospheric Chlorine and Fluorine Loading between 1985 and 1992

Mixing ratios of 3.44 ppbv (parts per billion by volume) and 1.23 ppbv for HCl and HF above 50 km, surrogates for total chlorine and fluorine, have been measured by the Atmospheric Trace Molecule Spectroscopy (ATMOS) experiment on a March 1992 flight of the Space Shuttle. Compared to the measured values obtained on a 1985 flight, these correspond to a 37% and 62% increase for HCl and HF, respectively. The derived trend in HCl (approx. 0.13 ppbv per year) is in good agreement with the model-predicted increase in chlorine loading of 0.13 ppbv per year, and with the measured trends in HCl total column abundance from reported ground-based observations. The main source of this change can be attributed to the release of man-made chlorofluorocarbons (CFC's) and hydro-chloro-fluoro-carbons (HCFC's). This new value for HCl represents an upper limit to the inorganic chlorine concentration in the stratosphere available for participation in photochemical processes which destroy ozone.

Gunson, M. R.↗

Time Resolved Visualization of A Liquid Jet in an RDE Using MHz Rate Diesel PLIF

The characterization of the dynamic response of liquid jets to transient detonation wave passage is critical for optimization and modeling of liquid fueled rotating detonation combustors. In this work, a rotating detonation combustor (RDC) is operated on hydrogen and air to sustain stable detonation waves that acts as a detonation driver and interact in a one-way coupled manner with a single liquid fuel jet that propagates into the combustion chamber with cycle periods of ~ 250 μs. Diesel is utilized as a realistic fuel surrogate with higher aromatic compounds to enable fluorescence excitation, using the 355 nm third harmonic output of a burst-mode Nd:YAG laser, imaged at rates up to 1 MHz. By optimizing the technique to accommodate orders of magnitude variations in the fuel density throughout the injection process, the PLIF data enable quantitative measurements including the refill time, the relative recovery between liquid and gaseous jets and jet trajectory across various momentum flux ratio. As the passage of the detonation wave imparts significant changes in the momentum flux ratio, the qualitative liquid break-up process and spatial distribution varies significantly in time. As the injection system recovers ~ 70% of the cycle period and return to a quasi-steady position and allow comparisons with theoretical jet trajectories. These data, enabled by ultra-high-speed PLIF imaging, represent some of the first detailed measurements for quantifying the dynamic response and recovery of liquid jets exposed to periodic detonations in an operating RDC.

Propulsion↗

Time Resolved Visualization of Liquid Jet Interaction With H2-Air Rotating Detonations Using MHz Rate Diesel PLIF

The characterization of the dynamic response of liquid jets to transient detonation wave passage is critical for optimization and modeling of liquid fueled rotating detonation combustors. In this work, a rotating detonation combustor (RDC) is operated on hydrogen and air to sustain stable detonation waves that acts as a detonation driver and interact in a one-way coupled manner with a single liquid fuel jet that propagates into the combustion chamber with cycle periods of ~ 250 μs. Diesel is utilized as a realistic fuel surrogate with higher aromatic compounds to enable fluorescence excitation, using the 355 nm thirdharmonic output of a burst-mode Nd:YAG laser, imaged at rates up to 1 MHz. By optimizing the technique to accommodate orders of magnitude variations in the fuel density throughout the injection process, the PLIF data enable quantitative measurements including the refill time, the relative recovery between liquid and gaseous jets and jet trajectory across various momentum flux ratio. As the passage of the detonation wave imparts significant changes in the momentum flux ratio, the qualitative liquid break-up process and spatial distribution varies significantly in time. As the injection system recovers ~ 70% of the cycle period and return to a quasi-steady position and allow comparisons with theoretical jet trajectories. These data, enabled by ultra-high-speed PLIF imaging, represent some of the first detailed measurements for quantifying the dynamic response and recovery of liquid jets exposed to periodic detonations in an operating RDC.

Propulsion↗

Stress Intensity Factors for Layered Pressure Vessel Inner Layer Through Cracks

A difficulty encountered when performing Fitness-for- Service assessments for layered pressure vessels (LPVs) is the lack of stress intensity factor solution in literature that produce accurate results for inner layer longitudinal through cracks. Using surrogate solutions such as a through crack in a plate or cylinder produce results that can be overly conservative especially for longer cracks. This is largely due to the ability of a layered pressure vessel to redistribute hoop load to other layers, the restricted radial movement of the cracked layer, and the friction forces applied in the cracked region. To understand this problem, a parametric finite element model (FEM) generator was developed that is capable of producing layered pressure vessel models with inner layer through cracks. The results from the FEMs were used to create a dataset of inner layer through crack stress intensity factors (KI) for layered pressure vessels corresponding to variations of internal pressure, radius, layer thicknesses, friction factor, and crack length. The elastic modulus of the material also has an effect on KI but, for this dataset, the elastic modulus was fixed at the typical value for steel - 29,500 ksi (203 GPa). Finally, a non-dimensional model was developed and calibrated using the dataset. This allows KI to be calculated without the need of a FEM using a closed-form equation. The results of the closed-form solution were then compared to FEM results showing accuracy was generally within 10%.

Hobbs, Joel R.↗

Multiphase Flow Technology Impacts on Thermal Control Systems for Exploration

The Two-Phase Flow Facility (TPHIFFy) Project focused on bridging the critical knowledge gap by developing and demonstrating critical multiphase fluid products for advanced life support, thermal management and power conversion systems that are required to enable the Vision for Space Exploration. Safety and reliability of future systems will be enhanced by addressing critical microgravity fluid physics issues associated with flow boiling, condensation, phase separation, and system stability. The project included concept development, normal gravity testing, and reduced gravity aircraft flight campaigns, in preparation for the development of a space flight experiment implementation. Data will be utilized to develop predictive models that could be used for system design and operation. A single fluid, two-phase closed thermodynamic loop test bed was designed, assembled and tested. The major components in this test bed include: a boiler, a condenser, a phase separator and a circulating pump. The test loop was instrumented with flow meters, thermocouples, pressure transducers and both high speed and normal speed video cameras. A low boiling point surrogate fluid, FC-72, was selected based on scaling analyses using preliminary designs for operational systems. Preliminary results are presented which include flow regime transitions and some observations regarding system stability.

McQuillen, John↗

A Dedicated, Long Duration Balloon Mission from Antarctica to Measure the Effects of Low Dose Galactic Cosmic Radiation on Biology

Antarctic long duration balloon missions flown by NASA’s Science Mission Directorate (SMD)can be used as a surrogate for the deep space radiation environment, reducing the need to launch orbital experiments to assess the impact of galactic cosmic radiation (GCR) on biology. To date, over fifty NASA balloon missions flown from Antarctica have carried scientific payloads from Astrophysics (APD) and Heliophysics (HPD)in SMD. Only two life science experiments have been flown from Antarctica, and both were ride-along (piggyback) opportunities, limiting the sophistication and types of model organisms that can be incorporated into studies. Herein, we argue for establishing a large, dedicated Antarctic balloon mission for the Biological and Physical Sciences (BPS) Division in SMD to be launched in 2029/2030, with an “omnibus” gondola carrying dozens of independent Space Biology payloads that would receive a sustained exposure to low dose rate GCRs for 30+ days. Our unprecedented, protracted radiation experiment cannot be done using ground-based simulation facilities or in space; it can only be achieved through an Antarctic balloon mission dedicated to BPS Division payloads. By providing more access to radiation research platforms through existing NASA SMD access to Antarctic balloon flight opportunities, the Space Biology community will be better positioned to address unknowns associated with low dose rate GCR exposures in long duration spaceflight.

David J Smith↗

An investigation of the role of current and future remote sensing data systems in numerical meteorology

The goals of this research endeavor have been to develop a flexible and relatively complete framework for the investigation of current and future satellite data sources in numerical meteorology. In order to realistically model how satellite information might be used for these purposes, it is necessary that Observing System Simulation Experiments (OSSEs) be as complete as possible. It is therefore desirable that these experiments simulate in entirety the sequence of steps involved in bringing satellite information from the radiance level through product retrieval to a realistic analysis and forecast sequence. In this project we have worked to make this sequence realistic by synthesizing raw satellite data from surrogate atmospheres, deriving satellite products from these data and subsequently producing analyses and forecasts using the retrieved products. The accomplishments made in 1991 are presented. The emphasis was on examining atmospheric soundings and microphysical products which we expect to produce with the launch of the Advanced Microwave Sounding Unit (AMSU), slated for flight in mid 1994.

Diak, George R.↗

Aircraft Conflict Analysis and Real-Time Conflict Probing Using Probabilistic Trajectory Modeling

Methods for maintaining separation between aircraft in the current airspace system have been built from a foundation of structured routes and evolved procedures. However, as the airspace becomes more congested and the chance of failures or operational error become more problematic, automated conflict alerting systems have been proposed to help provide decision support and to serve as traffic monitoring aids. The problem of conflict detection and resolution has been tackled from a number of different ways, but in this thesis, it is recast as a problem of prediction in the presence of uncertainties. Much of the focus is concentrated on the errors and uncertainties from the working trajectory model used to estimate future aircraft positions. The more accurate the prediction, the more likely an ideal (no false alarms, no missed detections) alerting system can be designed. Additional insights into the problem were brought forth by a review of current operational and developmental approaches found in the literature. An iterative, trial and error approach to threshold design was identified. When examined from a probabilistic perspective, the threshold parameters were found to be a surrogate to probabilistic performance measures. To overcome the limitations in the current iterative design method, a new direct approach is presented where the performance measures are directly computed and used to perform the alerting decisions. The methodology is shown to handle complex encounter situations (3-D, multi-aircraft, multi-intent, with uncertainties) with relative ease. Utilizing a Monte Carlo approach, a method was devised to perform the probabilistic computations in near realtime. Not only does this greatly increase the method's potential as an analytical tool, but it also opens up the possibility for use as a real-time conflict alerting probe. A prototype alerting logic was developed and has been utilized in several NASA Ames Research Center experimental studies.

Yang, Lee C.↗

A Computational Investigation of Sooting Limits of Spherical Diffusion Flames

Limiting conditions for soot particle inception in spherical diffusion flames were investigated numerically. The flames were modeled using a one-dimensional, time accurate diffusion flame code with detailed chemistry and transport and an optically thick radiation model. Seventeen normal and inverse flames were considered, covering a wide range of stoichiometric mixture fraction, adiabatic flame temperature, and residence time. These flames were previously observed to reach their sooting limits after 2 s of microgravity. Sooting-limit diffusion flames with residence times longer than 200 ms were found to have temperatures near 1190 K where C/O = 0.6, whereas flames with shorter residence times required increased temperatures. Acetylene was found to be a reasonable surrogate for soot precursor species in these flames, having peak mole fractions of about 0.01.

Lecoustre, V. R.↗

A Comparison of the Noise Characteristics of a Conventional Slat and Krueger Flap

An aeroacoustic test of two types of leading-edge high-lift devices has been conducted in the NASA Langley Quiet Flow Facility. The test compares a conventional slat with a notional equivalent-mission Krueger flap. The test matrix includes points that allow for direct comparison of the conventional and Krueger devices for equivalent-mission configurations, where the two high-lift devices satisfy the same lift requirements for a free air flight path at the same cruise airfoil angle of attack. Measurements are made for multiple Mach numbers and directivity angles. Results indicate that the Krueger flap shows similar agreement to the expected power law scaling of a conventional flap, both in terms of Strouhal number and fixed frequency (as a surrogate for Helmholtz number). Directivity patterns vary depending on the specific slat and Krueger orientations. Varying the slat gap while holding overlap constant has the same influence on both the conventional slat and Krueger flap acoustic signature. Closing the gap shows dramatic reduction in levels for both devices. Varying the Krueger overlap has a different effect on the data when compared to varying the slat overlap, but analysis is limited by acoustic sources that regularly present themselves in model-scale wind tunnel testing but are not present for full-scale vehicles. The Krueger cavity is found to have some influence on level and directivity, though not as much as the other considered parameter variations. Overall, while the spectra of the two devices are different in detail, their scaling behavior for varying parameters is extremely similar.

Bahr, Christopher J.↗

Diagnosis of Magnetic Structures and Intermittency in Space Plasma Turbulence using the Method of Surrogate Data

Several observations in space plasmas have reported the presence of coherent structures at different plasma scales. Structure formation is believed to be a direct consequence of nonlinear interactions between the plasma modes, which depend strongly on phase synchronization of those modes. Despite this important role of the phases in turbulence, very limited work has been however devoted to study the phases as a potential tracers of nonlinearities in comparison with the wealth of literature on power spectra of turbulence where phases are totally missed. We present a method based on surrogate data to systematically detect coherent structures in turbulent signals. The new method has been applied successfully to magnetosheath turbulence (Sahraoui, Phys. Rev. E, 2008, in press), where the relationship between the identified phase coherence and intermittency (classically identified as non Gaussian tails of the PDFs) as well as the energy cascade has been studied. Here we review the main results obtained in that study and show further applications to small scale solar wind turbulence. Implications of the results on theoretical modelling of space turbulence (applicability of weak/wave turbulence, its validity limits and its connection to intermittency) will be discussed.

Sahraoui, Fouad↗

NSCOR for Evaluating Risk Factors and Biomarkers for Adaptation and Resilience to Spaceflight: Emotional Valence and Social Processes in ICC/ICE Environments

Space exploration class missions, such as a mission to Mars, will require optimization of human performance, adaptability, and resilience. This NASA Specialized Center of Research (NSCOR) utilizes the NIMH Research Domain Criteria (RDoC) framework to identify biological and behavioral markers of individual social adaptation and emotional resilience (as well as vulnerability) to spaceflight-relevant stressors such as living in extended isolation. The overarching goal of this NSCOR is to obtain novel information to help identify biomarkers of individuals who are resilient and/or adaptable to the stressors of isolated, confined, and controlled (ICC) and isolated, confined, and extreme (ICE) environments.A total of N=90 healthy adult astronaut surrogates are being studied in three spaceflight-analog environments: (1) n=40 healthy adults in the Isolation and Confinement Analog Research Unit (ICARUS), an ICC at the University of Pennsylvania, during 7-day missions, for a target total of 280 subject days; (2) n=32 healthy adult astronaut surrogates studied in NASA’s Human Exploration Research Analog (HERA), an ICC at Johnson Space Center during 45-day missions, for a target total of 2,112 subject days; and (3) n=18 healthy adults in the Alfred-Wegener-Institute’s Neumayer Station III, an ICE in Antarctica, during 14-month missions, for a target total of 7,560 subject days. Dr. Nindl’s Laboratory at the University of Pittsburgh is analyzing a priori selected protein biomarkers in blood, saliva, and urine. Complementary rodent models of exposure to early life stressors, confinement, and isolation are being evaluated at Dr. Hensch’s Laboratory to further validate the neurobehavioral and biological findings from the human studies.Given the inconsistency and varied definition of resilience/adaptation in the scientific literature, the NSCOR team developed a composite resilience/adaptation measure that reflects the most relevant outcomes to resilience/adaptation across psychosocial and neurobehavioral functions, as well as neurocognitive and spaceflight-relevant operational performance. To achieve this, group consensus was attained from subject matter experts to produce a rank-order of importance for each input variable. The final resilience/adaptation score included 36 variables that were collected across spaceflight analogs. As of 10/1/2021, the NSCOR project acquired data on n=27 subjects at ICARUS, n=16 at HERA, and n=18 at Neumayer. The COVID-19 pandemic delayed data acquisition at ICARUS and HERA.Among subjects studied to date, 99% of neural and neurobehavioral data (e.g., neuroimaging for structure and function, behavioral measures) as well as blood, saliva, and urine for biochemical assays have been acquired. For rodent models, Dr. Hensch’s laboratory has established biochemical and behavioral parameters reflecting confinement stress in social networks of mice for comparison to stress responses in the human spaceflight analog environments.Group social behaviors were measured with a Social Network Analysis (SNA) approach to define objective parameters associated with sociability and its plasticity by sex. This analytic approach may help identify a network of individuals who are more effective teammates or more likely to generate new social relationships. Data acquisition, biomarker assessment, and data quality control will continue through September 2022.

D F Dinges↗

Directed Research in Bone Discipline: Refining Previous Research Observations for Space Medicine

Dual-energy X-ray absorptiometry bone mass density, as a sole index, is an insufficient surrogate for fracture; Clinical Practice Guidelines using bone mass density (both World Health Organization and FRAX) are not specific for complicated subjects such as young, healthy persons following prolonged exposure to skeletal unloading (i.e. an attribute of spaceflight); Research data suggest that spaceflight induces changes to astronaut bones that could be profound, possibly irreversible and unlike age-related bone loss on Earth.; There is a need to objectively assess factors across human physiology that are also influenced by spaceflight (e.g., muscle) that contribute to fracture risk. Some of these objective assessments may require innovative technologies, analyses and modeling.; Astronauts are also exposed to novel situations that may overload their bones highlighting a need integrate biomechanics of physical activities into risk assessments.; As we accumulate data, which reflects the biomechanical competence of bone under specific mechanically-loaded scenarios (even activities of daily living), BONE expects Bone Fracture Module to be more sensitive and/or have less uncertainty in its assessments of fracture probability.; Fracture probability drives the requirement for countermeasures. Level of evidence will unlikely be obtained; hence, the Bone Research and Clinical Advisory Panel (like a Data Safety Monitoring Board) will provide the recommendations.

Sibonga, Jean D.↗

Electrorheological Fluid Based Force Feedback Device

Parallel to the efforts to develop fully autonomous robots, it is increasingly being realized that there are applications where it is essential to have a fully controlled robot and "feel" its operating conditions, i.e. telepresence. This trend is a result of the increasing efforts to address tasks where humans can perform significantly better but, due to associated hazards, distance, physical limitations and other causes, only robots can be employed to perform these tasks. Such robots need to be assisted by a human that remotely controls the operation. To address the goal of operating robots as human surrogates, the authors launched a study of mechanisms that provide mechanical feedback. For this purpose, electrorheological fluids (ERF) are being investigated for the potential application as miniature haptic devices. This family of electroactive fluids has the property of changing the viscosity during electrical stimulation. Consequently, ERF can be used to produce force feedback haptic devices for tele-operated control of medical and space robotic systems. Forces applied at the robot end-effector due to a compliant environment are reflected to the user using an ERF device where a change in the system viscosity will occur proportionally to the transmitted force. Analytical model and control algorithms are being developed taking into account the non-linearities of these type of devices. This paper will describe the concept and the developed mechanism of ERF based force feedback. The test process and the physical properties of this device will be described and the results of preliminary tests will be presented.

Pfeiffer, Charles↗

Left ventricular outflow tract mean systolic acceleration as a surrogate for the slope of the left ventricular end-systolic pressure-volume relationship

OBJECTIVE: The goal of this study was to analyze left ventricular outflow tract systolic acceleration (LVOT(Acc)) during alterations in left ventricular (LV) contractility and LV filling. BACKGROUND: Most indexes described to quantify LV systolic function, such as LV ejection fraction and cardiac output, are dependent on loading conditions. METHODS: In 18 sheep (4 normal, 6 with aortic regurgitation, and 8 with old myocardial infarction), blood flow velocities through the LVOT were recorded using conventional pulsed Doppler. The LVOT(Acc) was calculated as the aortic peak velocity divided by the time to peak flow; LVOT(Acc) was compared with LV maximal elastance (E(m)) acquired by conductance catheter under different loading conditions, including volume and pressure overload during an acute coronary occlusion (n = 10). In addition, a clinically validated lumped-parameter numerical model of the cardiovascular system was used to support our findings. RESULTS: Left ventricular E(m) and LVOT(Acc) decreased during ischemia (1.67 +/- 0.67 mm Hg.ml(-1) before vs. 0.93 +/- 0.41 mm Hg.ml(-1) during acute coronary occlusion [p < 0.05] and 7.9 +/- 3.1 m.s(-2) before vs. 4.4 +/- 1.0 m.s(-2) during coronary occlusion [p < 0.05], respectively). Left ventricular outflow tract systolic acceleration showed a strong linear correlation with LV E(m) (y = 3.84x + 1.87, r = 0.85, p < 0.001). Similar findings were obtained with the numerical modeling, which demonstrated a strong correlation between predicted and actual LV E(m) (predicted = 0.98 [actual] -0.01, r = 0.86). By analysis of variance, there was no statistically significant difference in LVOT(Acc) under different loading conditions. CONCLUSIONS: For a variety of hemodynamic conditions, LVOT(Acc) was linearly related to the LV contractility index LV E(m) and was independent of loading conditions. These findings were consistent with numerical modeling. Thus, this Doppler index may serve as a good noninvasive index of LV contractility.

Non-NASA Center↗

Probability Bounds Analysis Applied to Multi-Purpose Crew Vehicle Nonlinearity

The Multi-Purpose Crew Vehicle (MPCV) Program Orion vehicle finite element model (FEM) was updated based on a modal test performed by Lockheed Martin. Due to nonlinearity observed in the test results, linear low force level (LL) and high force level (HL) FEMs were developed for use during various Space Launch System (SLS) flight regimes depending on expected forcing levels. Uncertainty models were derived for the combined MPCV and MPCV Stage Adaptor LL and HL Hurty/Craig-Bampton (HCB) components based on the MPCV structural test article Configuration 4 modal test-analysis correlation results. Subsequently, system-level uncertainty quantification analyses were performed using both models for various SLS flight configurations to determine the impact of the nonlinearity on important system metrics. The system metrics included both transfer functions associated with attitude control and dynamic loads associated with aerodynamic buffeting during ascent. In each case, an independent Monte Carlo (MC) analysis was performed, and no attempt was made to combine the results. The Hybrid Parametric Variation (HPV) method was used to develop the LL and HL MPCV HCB uncertainty models. The HPV method provides both parametric and non-parametric components of uncertainty. The non-parametric uncertainty accounts for the difference in model-form between the linearized analytical model and the corresponding linearized component test results in the form of mode shapes and frequencies at that force level. This linear model-form uncertainty is implemented in the HPV method using random matrix theory. However, the HPV uncertainty models developed for the linear LL and HL MPCV components do not account for the nonlinearity in the MPCV. With respect to the linearized models, this nonlinearity is also an uncertainty in model form, but in this case, it must be treated independently as an epistemic uncertainty. It represents a lack of knowledge, in contrast to an aleatory uncertainty due to the randomness of a variable. In the case of an epistemic variable, the true value is unknown, only the interval within which it lies is known. Epistemic uncertainty can be reduced with increased knowledge, while in general, aleatory uncertainty cannot. This work combines the epistemic uncertainty due to the MPCV nonlinearity with the parametric and non-parametric uncertainty within the HPV method using a second order propagation approach. The LL and HL test data is augmented with surrogate test data derived from a nonlinear MPCV representation. The impact of the MPCV nonlinearity on system response statistics is determined using a series of cumulative distribution functions in the form of a horsetail plot, or p-box. This results in an interval of probabilities for a specific response value, or an interval of response values at a specific probability.

Daniel C Kammer↗

An analysis of the relationship between cloud anomalies and sea surface temperature anomalies in a global circulation model

The relationship between the sea surface temperature anomalies (SSTAs) and the anomalies of the monthly mean cloud cover (including the high-level, low-level, and total cloud cover), the outgoing longwave radiation, and the reflected solar radiation was analyzed using a least absolute deviations regression at each grid point over the open ocean for a 6-yr period. The results indicate that cloud change in association with a local 1-C increase in SSTAs cannot be used to predict clouds in a potential future world where all the oceans are 1-C warmer than at present, because much of the observed cloud changes are due to circulation changes, which in turn are related not only to changes in SSTAs but to changes in SSTA gradients. However, because SSTAs are associated with changes in the local ocean-atmosphere moisture and heat fluxes as well as significant changes in circulation (such as ENSO), SSTAs can serve as a surrogate for many aspects of global climate change.

Peterson, Thomas C.↗

Multifractal scaling of the kinetic energy flux in solar wind turbulence

The geometrical and scaling properties of the energy flux of the turbulent kinetic energy in the solar wind have been studied. By present experimental technology in solar wind measurements, we cannot directly measure the real volumetric dissipation rate, epsilon(t), but are constrained to represent it by surrogating the energy flux near the dissipation range at the proton gyro scales. There is evidence for the multifractal nature of the so defined dissipation field epsilon(t), a result derived from the scaling exponents of its statistical q-th order moments. The related generalized dimension D(q) has been determined and reveals that the dissipation field has a multifractal structure. which is not compatible with a scale-invariant cascade. The associated multifractal spectrum f(alpha) has been estimated for the first time for MHD turbulence in the solar wind. Its features resemble those obtained for turbulent fluids and other nonlinear multifractal systems. The generalized dimension D(q) can, for turbulence in high-speed streams, be fitted well by the functional dependence of the p-model with a comparatively large parameter, p = 0.87. indicating a strongly intermittent multifractal energy cascade. The experimental value for D(p)/3, if used in the scaling exponent s(p) of the velocity structure function, gives an exponent that can describe some of the observations. The scaling exponent mu of the auto correlation function of epsilon(t) has also been directly evaluated. It has the value of 0.37. Finally. the mean dissipation rate was determined, which could be used in solar wind heating models.

Marsch, E.↗