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Relativistic particle acceleration in plerions

We discuss recent research on the structure and particle acceleration properties of relativistic shock waves in which the magnetic field is transverse to the flow direction in the upstream medium, and whose composition is either pure electrons and positrons or primarily electrons and positrons with an admixture of heavy ions. Particle-in-cell simulation techniques as well as analytic theory have been used to show that such shocks in pure pair plasmas are fully thermalized -- the downstream particle spectra are relativistic Maxwellians at the temperature expected from the jump conditions. On the other hand, shocks containing heavy ions which are a minority constituent by number but which carry most of the energy density in the upstream medium do put approximately 20% of the flow energy into a nonthermal population of pairs downstream, whose distribution in energy space is N(E) varies as E(exp -2), where N(E)dE is the number of particles with energy between E and E+dE. The mechanism of thermalization and particle acceleration is found to be synchrotron maser activity in the shock front, stimulated by the quasi-coherent gyration of the whole particle population as the plasma flowing into the shock reflects from the magnetic field in the shock front. The synchrotron maser modes radiated by the heavy ions are absorbed by the pairs at their (relativistic) cyclotron frequencies, allowing the maximum energy achievable by the pairs to be gamma(sub +/-)m(sub +/-)c squared = m(sub i)c squared gamma(sub 1)/Z(sub i), where gamma(sub 1) is the Lorentz factor of the upstream flow and Z(sub i) is the atomic number of the ions. The shock's spatial structure is shown to contain a series of 'overshoots' in the magnetic field, regions where the gyrating heavy ions compress the magnetic field to levels in excess of the eventual downstream value. This shock model is applied to an interpretation of the structure of the inner regions of the Crab Nebula, in particular to the 'wisps,' surface brightness enhancements near the pulsar. We argue that these surface brightness enhancements are the regions of magnetic overshoot, which appear brighter because the small Larmor radius pairs are compressed and radiate more efficiently in the regions of more intense magnetic field. This interpretation suggests that the structure of the shock terminating the pulsar's wind in the Crab Nebula is spatially resolved, and allows one to measure gamma(sub 1) and a number of other properties of the pulsar's wind. We also discuss applications of the shock theory to the termination shocks of the winds from rotation-powered pulsars embedded in compact binaries. We show that this model adequately accounts for (and indeed predicted) the recently discovered X-ray flux from PSR 1957+20, and we discuss several other applications to other examples of these systems.

Arons, Jonathan↗

Effects of microgravity and clinorotation on stress ethylene production in two starchless mutants of Arabidopsis thaliana

Starch filled plastids termed amyloplasts, contained within columella cells of the root caps of higher plant roots, are believed to play a statolith-like role in the gravitropic response of roots. Plants having amyloplasts containing less starch exhibit a corresponding reduction in gravitropic response. We have observed enhanced ethylene production by sweet clover (Melilotus alba L.) seedlings grown in the altered gravity condition of a slow rotating clinostat, and have suggested that this is a stress response resulting from continuous gravistimulation rather than as a result of the simulation of a microgravity condition. If so, we expect that plants deficient in starch accumulation in amyloplasts may produce less stress ethylene when grown on a clinostat. Therefore, we have grown Arabidopsis thaliana in the small, closed environment of the Fluid Processing Apparatus (FPA). In this preliminary report we compare stationary plants with clinorotated and those grown in microgravity aboard Discovery during the STS-63 flight in February 1995. In addition to wildtype, two mutants deficient in starch biosynthesis, mutants TC7 and TL25, which are, respectively, deficient in the activity of amyloplast phosphoglucomutase and ADP-glucose pyrophosphorylase, were grown for three days before being fixed within the FPA. Gas samples were aspirated from the growth chambers and carbon dioxide and ethylene concentations were measured using a gas chromatograph. The fixed tissue is currently undergoing further morphologic and microscopic characterization.

Gallegos, Gregory L.↗

Preliminary Investigation of Impact on Multiple-Sheet Structures and an Evaluation of the Meteoroid Hazard to Space Vehicles

Small pyrex glass spheres, representative of stoney meteoroids, were fired into 2024-T3 aluminum alclad multiple-sheet structures at velocities to 11,000 feet per second to evaluate the effectiveness of multisheet hull construction as a means of increasing the resistance of a spacecraft to meteoroid penetrations. The results of these tests indicate that increasing the number of sheets in a structure while keeping the total sheet thickness constant and increasing the spacing between sheets both tend to increase the penetration resistance of a structure of constant weight per unit area. In addition, filling the space between the sheets with a light filler material was found to substantially increase structure penetration resistance with a small increase in weight. An evaluation of the meteoroid hazard to space vehicles is presented in the form of an illustrative-example for two specific lunar mission vehicles, a single-sheet, monocoque hull vehicle and a glass-wool filled, double-sheet hull vehicle. The evaluation is presented in terms of the "best" and the "worst" conditions that might be expected as determined from astronomical and satellite measurements, high-speed impact data, and hypothesized meteoroid structures and compositions. It was observed that the vehicle flight time without penetration can be increased significantly by use of multiple-sheet rather than single-sheet hull construction with no increase in hull weight. Nevertheless, it is evident that a meteoroid hazard exists, even for the vehicle with the selected multiple-sheet hull.

Nysmith, C. Robert↗

The Recovery of TOMS-EP

On December 13th 1998, the Total Ozone Mapping Spectrometer - Earth Probe (TOMS-EP) spacecraft experienced a Single Event Upset which caused the system to reconfigure and enter a Safe Mode. This incident occurred two and a half years after the launch of the spacecraft which was designed for a two year life. A combination of factors, including changes in component behavior due to age and extended use, very unfortunate initial conditions and the safe mode processing logic prevented the spacecraft from entering its nominal long term storage mode. The spacecraft remained in a high fuel consumption mode designed for temporary use. By the time the onboard fuel was exhausted, the spacecraft was Sun pointing in a high rate flat spin. Although the uncontrolled spacecraft was initially in a power and thermal safe orientation, it would not stay in this state indefinitely due to a slow precession of its momentum vector. A recovery team was immediately assembled to determine if there was time to develop a method of despinning the vehicle and return it to normal science data collection. A three stage plan was developed that used the onboard magnetic torque rods as actuators. The first stage was designed to reduce the high spin rate to within the linear range of the gyros. The second stage transitioned the spacecraft from sun pointing to orbit reference pointing. The final stage returned the spacecraft to normal science operation. The entire recovery scenario was simulated with a wide range of initial conditions to establish the expected behavior. The recovery sequence was started on December 28th 1998 and completed by December 31st. TOMS-EP was successfully returned to science operations by the beginning of 1999. This paper describes the TOMS-EP Safe Mode design and the factors which led to the spacecraft anomaly and loss of fuel. The recovery and simulation efforts are described. Flight data are presented which show the performance of the spacecraft during its return to science. Finally, lessons learned are presented.

Robertson, Brent↗

Wintertime East Asian Jet Stream and its Association with the Asian-Pacific-American Climate

The wintertime upper-tropospheric westerly jet stream over subtropical East Asia and western Pacific, often referred to as East Asian Jet (EAJ), is an important atmospheric circulation system in the Asian-Pacific-American (APA) region. It is characterized by variabilities on a wide range of time scales and exerts a strong impact on the weather and climate of the region. On the synoptic scale, the jet is closely linked to many phenomena such as cyclogenesis, frontogenesis, blocking, storm track activity, and the development of other atmospheric disturbances. On the seasonal time scale, the variation of the EAJ determines many characteristics of the seasonal transition of the atmospheric circulation over Asia. The variabilities of the jet on these time scales have been relatively well documented (e.g., Yeh et al. 1959, Palmen and Newton 1969; Zeng 1979). It has also been understood that the inter-annual variability of the EAJ is associated with many climate signals in the APA region. These signals include the persistent anomalies of the East Asian winter monsoon and the changes in diabatic heating and in the Hadley circulation (Bjerknes 1966; Chang and Lau 1980; Huang and Gambo 1982; Kang and Held 1986; Tao and Chen 1987; Lau et al. 1988; Yang and Webster 1990; Ding 1992; Webster and Yang 1992; Dong et al. 1999). However, many questions remain for the year-to-year variabilities of the jet and their relation to the APA climate. For example, what is the relationship between the EAJ and El Nino/Southern Oscillation (ENSO)? Will the jet and ENSO play different roles in modulating the APA climate? How is the jet linked to North Pacific sea surface temperature (SST) and the Pacific/North American (PNA) teleconnection pattern? In this study, we address several issues related to the wintertime EAJ with a focus on interannual time scales. We will examine the association between the jet core and ENSO, which has always been overshadowed by the relationship between ENSO and the upper-tropospheric winds over northern extratropics of the central Pacific. We will investigate the linkage of the jet to variabilities of the Asian winter monsoon, tropical convection, and upper tropospheric wave patterns. We will also explore the relationship between the jet core and extratropical S ST with an aim at providing helpful information for improving our understanding of the connection of the EAJ to surface boundary conditions. The analysis is expected to provide information that is helpful for improving regional climate predictions.

Yang, Song↗

Managing Risk for Thermal Vacuum Testing of the International Space Station Radiators

The International Space Station (ISS) is designed with large deployable radiator panels that are used to reject waste heat from the habitation modules. Qualification testing of the Heat Rejection System (HRS) radiators was performed using qualification hardware only. As a result of those tests, over 30 design changes were made to the actual flight hardware. Consequently, a system level test of the flight hardware was needed to validate its performance in the final configuration. A full thermal vacuum test was performed on the flight hardware in order to demonstrate its ability to deploy on-orbit. Since there is an increased level of risk associated with testing flight hardware, because of cost and schedule limitations, special risk mitigation procedures were developed and implemented for the test program, This paper introduces the Continuous Risk Management process that was utilized for the ISS HRS test program. Testing was performed in the Space Power Facility at the NASA Glenn Research Center, Plum Brook Station located in Sandusky, Ohio. The radiator system was installed in the 100-foot diameter by 122-foot tall vacuum chamber on a special deployment track. Radiator deployments were performed at several thermal conditions similar to those expected on-orbit using both the primary deployment mechanism and the back-up deployment mechanism. The tests were highly successful and were completed without incident.

Carek, Jerry A.↗

Using the Human Eye to Characterize Displays

Monitor characterization has taken on new importance for non-professional users, who are not usually equipped to make photometric measurements. We studied adjusting brightness to set the black level, banding effects due to digitization, and gamma estimation in the light and in the dark, and a color-matching task in the light, on a desktop CRT (Cathode-Ray Tube) and a laptop LCD (Liquid Crystal Display). Observers demonstrated the sensitivity of the visual system for comparative judgments in black-level adjustment, banding visibility, and gamma estimation. The results of the color-matching task were ambiguous. In the brightness adjustment task, the action of the adjustment was not as presumed; however, perceptual judgments were as expected under the actual conditions. When the gamma estimates of observers were compared to photometric measurements, problems with the definition of gamma were identified. Information about absolute light levels that would be important for characterizing a displays, given the shortcomings of gamma in measuring apparent contrast, are not measurable by eye alone. The LCD was not studied as extensively as the CRT because of viewing-angle problems, and its transfer function did not follow a power law, rendering gamma estimation meaningless.

Gille, Jennifer↗

Satellite Ocean Color Validation Using Merchant Ships

A collaborative measurement program for evaluating satellite-derived ocean color has been developed based on ships of opportunity (merchant, oceanographic) and specific instrumentation, the SIMBAD radiometer. The purpose of the measurement program is to complement, in a cost-effective way, dedicated evaluation experiments at sea, which are expensive, cannot be carried out over the full range of expected oceanic and atmospheric conditions, and generally provide a few match-ups. Ships participate in the program on a volunteer basis or at a very small cost, and measurement procedures do not interfere with other ship activities. The SIMBAD radiometer is a portable, easy-to-operate instrument that measures the basic ocean color variables, namely aerosol optical thickness and water-leaving radiance, in typical spectral bands of ocean-color sensors, i.e., 443, 490, 560, 670, and 870 nm. Measuring these variables at the time of satellite overpass is usually sufficient to verify satellite-derived ocean color and to evaluate atmospheric correction algorithms. Any ordinary crew can learn quickly how to make measurements. Importantly, the ship is not required to stop, making it possible to collect data along regular routes traveled by merchant ships in the world's oceans.

Frouin, Robert↗

Numerical Simulations of High Enthalpy Pulse Facilities

Axisymmetric flows within shock tubes and expansion tubes are simulated including the effects of finite rate chemistry and both laminar and turbulent boundary layers. The simulations demonstrate the usefulness of computational fluid dynamics for characterizing the flows in high enthalpy pulse facilities. The modeling and numerical requirements necessary to simulate these flows accurately are also discussed. Although there is a large body of analysis which explains and quantifies the boundary layer growth between the shock and the interface in a shock tube, there is a need for more detailed solutions. Phenomena such as thermochemical nonequilibrium. or turbulent transition behind the shock are excluded in the assumptions of Mirels' analysis. Additionally there is inadequate capability to predict the influence of the boundary layer on the expanded gas behind the interface. Quantifying the gas in this region is particularly important in expansion tubes because it is the location of the test gas. Unsteady simulations of the viscous flow in shock tubes are computationally expensive because they must follow features such as a shock wave over the length of the facility and simultaneously resolve the small length scales within the boundary layer. As a result, efficient numerical algorithms are required. The numerical approach of the present work is to solve the axisymmetric gas dynamic equations using an finite-volume formulation where the inviscid fluxes are computed with a upwind TVD scheme. Multiple species equations are included in the formulation so that finite-rate chemistry can be modeled. The simulations cluster grid points at the shock and interface and translate this clustered grid with these features to minimize numerical errors. The solutions are advanced at a CFL number of less than one based on the inviscid gas dynamics. To avoid limitations on the time step due to the viscous terms, these terms are treated implicitly. This requires a block tri-diagonal matrix inversion along each line of cells normal to the wall. The cost of this inversion is more than offset by the larger allowable time step. The source terms representing the finite-rate chemical kinetics are also treated implicitly. An algebraic turbulence model for compressible flow is used. The flow in a low pressure shock tube is computed and the results are compared with Mirels'analysis. The driven gas is nitrogen at 70 Pa, and the incident shock speed is approximately 2.9 km/sec so that there is little dissociation. The simulations include a laminar boundary layer and are run until the limiting flow regime is achieved. At this limit, the shock and interface travel at the same velocity because the amount of driven gas between these two features remains the same: the mass flow across the shock is equal to the mass of gas being entrained at the interface by the boundary layer. Simulations with several grids are presented to establish the grid independence of the solution, Good agreement is achieved between Mirels' correlations and the computations. This is expected since the flow conditions are chosen to be consistent with the assumptions used in Mirels' analysis. This comparison adds credibility to the numerical approach and highlights some of the differences between the theory and the detailed simulations. In addition, simulations of the HYPULSE expansion tube are presented for two operating conditions and the computations are compared to experimental data. The operating gas for both cases is nitrogen. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium. in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a pressure of 38 kPa and is characterized by a turbulent boundary layer. The simulations compare well with experiment and reveal that the nonuniformity in pressure observed during the test time is related to variations in the boundary layer displacement thickness.

Wilson, Gregory J.↗

Laboratory Studies of the Photochemistry of Peroxynitric Acid

Observations of odd hydrogen radicals at high SZA in the lower stratosphere have demonstrated that our understanding of the HO(x) chemistry is incomplete [Wennberg et al., 1994a; Salawitch et al., 1994; Wennberg et al., 1999]. In particular, the concentrations of the HO(x) radicals are significantly larger than expected under weak photolytic conditions. Donaldson et al. [1997] have speculated that excitation of overtones of the OH stretching frequency in molecules such as HNO3 and HO2NO2 may be significant sources of HO(x) under these conditions. Although weak, vibrationally mediated photolysis may be important because it occurs in the near IR and visible and can provide energy in excess of the dissociation energy (D(o)): HONO2 + hv yields OH + NO (D(o) approx. 600 nm) and HOONO2 + hv yields OH + NO3 (D(o) approx. 735 nm) HOONO2 + hv yields HO2 + NO2 (D(o) approx. 1250 nm). In this project we developed instrumentation to characterize the photodissociation yields of hydroxyl containing compounds in the visible and near IR. This effort has involved coupling a tunable photolysis optical parametric oscillator (OPO) laser system with precise determination of the hydroxyl radical. The OPO system [Wu et al., 1997] was developed with support from the NSF Major Research Instrumentation Fund in a proposal entitled "Development of Novel, Compact Light Sources for Advanced Spectroscopy in Atmospheric Science and Materials Research" (Geoffrey A. Blake, P.I. California Institute of Technology).

Wennberg, Paul O.↗

Plasmaspheric Erosion via Plasmasphere Coupling to Ring Current Plasmas: EUV Observations and Modeling

During a geomagnetic storm on 24 May 2000, the IMAGE Extreme Ultraviolet (EUV) camera observed a plasmaspheric density trough in the evening sector at L-values inside the plasmapause. Forward modeling of this feature has indicated that plasmaspheric densities beyond the outer wall of the trough are well below model expectations. This diminished plasma condition suggests the presence of an erosion process due to the interaction of the plasmasphere with ring current plasmas. We present an overview of EUV, energetic neutral atom (ENA), and Far Ultraviolet (FUV) camera observations associated with the plasmaspheric density trough of 24 May 2000, as well as forward modeling evidence of the lie existence of a plasmaspheric erosion process during this period. FUV proton aurora image analysis, convolution of ENA observations, and ring current modeling are then presented in an effort to associate the observed erosion with coupling between the plasmasphere and ring-current plasmas.

Adrian, M. L.↗

Gamma Ray Large Area Space Telescope (GLAST) Balloon Flight Engineering Model: Overview

The Gamma Ray Large Area Space Telescope (GLAST) Large Area Telescope (LAT) is a pair-production high-energy (greater than 20 MeV) gamma-ray telescope being built by an international partnership of astrophysicists and particle physicists for a satellite launch in 2006, designed to study a wide variety of high-energy astrophysical phenomena. As part of the development effort, the collaboration has built a Balloon Flight Engineering Model (BFEM) for flight on a high-altitude scientific balloon. The BFEM is approximately the size of one of the 16 GLAST-LAT towers and contains all the components of the full instrument: plastic scintillator anticoincidence system (ACD), high-Z foil/Si strip pair-conversion tracker (TKR), CsI hodoscopic calorimeter (CAL), triggering and data acquisition electronics (DAQ), commanding system, power distribution, telemetry, real-time data display, and ground data processing system. The principal goal of the balloon flight was to demonstrate the performance of this instrument configuration under conditions similar to those expected in orbit. Results from a balloon flight from Palestine, Texas, on August 4, 2001, show that the BFEM successfully obtained gamma-ray data in this high-background environment.

Thompson, D. J.↗

Using the Human Eye to Characterize Displays

Monitor characterization has taken on new importance for non-professional users, who are not usually equipped to make photometric measurements. Our purpose was to examine some of the visual judgments used in characterization schemes that have been proposed for web users. We studied adjusting brightness to set the black level, banding effects due to digitization, and gamma estimation in the light and in the dark, and a color-matching task in the light, on a desktop CRT and a laptop LCD. Observers demonstrated the sensitivity of the visual system for comparative judgments in black-level adjustment, banding visibility, and gamma estimation. The results of the color-matching task were ambiguous. In the brightness adjustment task, the action of the adjustment was not as presumed; however, perceptual judgments were as expected under the actual conditions. When the gamma estimates of observers were compared to photometric measurements, problems with the definition of gamma were identified. Information about absolute light levels that would be important for characterizing a display, given the shortcomings of gamma in measuring apparent contrast, are not measurable by eye alone. The LCD was not studied as extensively as the CRT because of viewing-angle problems, and its transfer function did not follow a power law, rendering gamma estimation meaningless.

Gille, Jennifer↗

Evaluation of Low-Earth-Orbit Environmental Effects on International Space Station Thermal Control Materials

Many spacecraft thermal control coatings in low Earth orbit (LEO) can be affected by solar ultraviolet radiation and atomic oxygen. Ultraviolet radiation can darken some polymers and oxides commonly used in thermal control materials. Atomic oxygen can erode polymer materials, but it may reverse the ultraviolet-darkening effect on oxides. Maintaining the desired solar absorptance for thermal control coatings is important to assure the proper operating temperature of the spacecraft. Thermal control coatings to be used on the International Space Station (ISS) were evaluated for their performance after exposure in the NASA Lewis Research Center's Atomic Oxygen-Vacuum Ultraviolet Exposure (AO-VUV) facility. This facility simulated the LEO environments of solar vacuum ultraviolet (VUV) radiation (wavelength range, 115 to 200 nanometers (nm)) and VUV combined with atomic oxygen. Solar absorptance was measured in vacuo to eliminate the "bleaching" effects of ambient oxygen on VUV-induced degradation. The objective of these experiments was to determine solar absorptance increases of various thermal control materials due to exposure to simulated LEO conditions similar to those expected for ISS. Work was done in support of ISS efforts at the requests of Boeing Space and Defense Systems and Lockheed Martin Vought Systems.

Dever, Joyce A.↗

Automated mass spectrometer analysis system

An automated mass spectrometer analysis system is disclosed, in which samples are automatically processed in a sample processor and converted into volatilizable samples, or their characteristic volatilizable derivatives. Each volatilizable sample is sequentially volatilized and analyzed in a double focusing mass spectrometer, whose output is in the form of separate ion beams all of which are simultaneously focused in a focal plane. Each ion beam is indicative of a different sample component or different fragments of one or more sample components and the beam intensity is related to the relative abundance of the sample component. The system includes an electro-optical ion detector which automatically and simultaneously converts the ion beams, first into electron beams which in turn produce a related image which is transferred to the target of a vilicon unit. The latter converts the images into electrical signals which are supplied to a data processor, whose output is a list of the components of the analyzed sample and their abundances. The system is under the control of a master control unit, which in addition to monitoring and controlling various power sources, controls the automatic operation of the system under expected and some unexpected conditions and further protects various critical parts of the system from damage due to particularly abnormal conditions.

Kuppermann, Aron↗

Automated mass spectrometer analysis system

An automated mass spectrometer analysis system is disclosed, in which samples are automatically processed in a sample processor and converted into volatilizable samples, or their characteristic volatilizable derivatives. Each volatizable sample is sequentially volatilized and analyzed in a double focusing mass spectrometer, whose output is in the form of separate ion beams all of which are simultaneously focused in a focal plane. Each ion beam is indicative of a different sample component or different fragments of one or more sample components and the beam intensity is related to the relative abundance of the sample component. The system includes an electro-optical ion detector which automatically and simultaneously converts the ion beams, first into electron beams which in turn produce a related image which is transferred to the target of a vidicon unit. The latter converts the images into electrical signals which are supplied to a data processor, whose output is a list of the components of the analyzed sample and their abundances. The system is under the control of a master control unit, which in addition to monitoring and controlling various power sources, controls the automatic operation of the system under expected and some unexpected conditions and further protects various critical parts of the system from damage due to particularly abnormal conditions.

Boettger, Heinz G.↗

Evaluation of Sulfur 'Concrete' for Use as a Construction Material on the Lunar Surface

Combining molten sulfur with any number of aggregate materials forms, when solid, a mixture having attributes similar, if not better, to conventional water-based concrete. As a result the use of sulfur "concrete" on Earth is well established, particularly in corrosive environments. Consequently, discovery of troilite (FeS) on the lunar surface prompted numerous scenarios about its reduction to elemental sulfur for use, in combination with lunar regolith, as a potential construction material; not requiring water, a precious resource, for its manufacture is an obvious advantage. However, little is known about the viability of sulfur concrete in an environment typified by extreme temperatures and essentially no atmosphere. The experimental work presented here evaluates the response of pure sulfur and sulfur concrete subjected to laboratory conditions that approach those expected on the lunar surface, the results suggesting a narrow window of application.

Grugel, R. N.↗

The Stationary Condensation and Radial Outflow of a Liquid Film on a Horizontal Disk

The application of capillary screen liquid acquisition devices to space-based cryogenic propulsion systems is expected to necessitate thermodynamic conditioning in order to stabilize surface tension retention characteristics. The present results have been obtained in the framework of the research of low gravity condensation-flow processes for conditioning cryogenic liquid acquisition devices. The following system is studied: On the top of a subcooled horizontal disk, a liquid film condenses from the ambient saturated vapor. The liquid is forcedly removed at the disk edge, and there is an outward radial flow of the film. Stationary regimes of the flow are uncovered such that (i) the gravity is negligible, being eclipsed by the capillary forces; (ii) the film thickness is everywhere much smaller than the disk radius; and (iii) the slow-flow lubrication approximation is valid. A nonlinear differential equation for the film thickness as a function of the radial coordinate is obtained. The (two-dimensional) fields of velocities, temperature and pressure in the film are explicitly determined by the radial profile of its thickness. The equilibrium is controlled by two parameters: (i) the vapor-disk difference of temperatures and (ii) the liquid exhaust rate. For the flow regimes with a nearly uniform film thickness, the governing equation linearizes, and the film interface is analytically predicted to have a concave-up quartic parabola profile. Thus, perhaps counter-intuitively, the liquid film is thicker at the edge and thinner at the center of the disk.

Bolshinskiy, Leonid↗