SEARCH · Search NASA

Results for “STRATIFIED FLOW”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

All sources NASA NTRS DOE OSTI

NASA NTRS2000

Three-Dimensional Simulations of the Parker Instability in a Uniformly-Rotating Disk

We investigate the, nonlinear effects of uniform rotation on the Parker instability in an exponentially-stratified disk through high-resolution simulations. During the linear stage, the speed of gas motion is subsonic and the evolution with the rotation is not much different from that without the rotation. This is because the Coriolis force is small. During the nonlinear stage, oppositely-directed supersonic flows near a magnetic valley are under the influence of the Coriolis force with different directions, resulting in twisted magnetic field lines near the valley. Sheet-like structures, which are tilted with respect to the initial field direction, are formed with an 1.5 enhancement of column density with respect to its initial value. Even though uniform rotation doesn't give much impact on density enhancement, it generates helically twisted field lines, which may become an additional support mechanism of clouds.

Kim, Jongsoo↗

NASA NTRS2002

Transient Mixing Driven by Buoyancy Flows

Mixing driven by buoyancy-induced flows is of particular interest to microgravity processes, as the body force that governs the intensity of flow fields can be directly controlled. We consider a model experimental system to explore the dynamics of mixing which employs two miscible liquids inside a cavity separated initially by a divider. The two liquids are oriented vertically inside a rectangular cavity with constant width and height, and varying depths to span the range of a Hele-Shaw cell to a 3-[) configuration. The two miscible liquids can be sufficiently diluted and died, for example water and deuterium oxide, such that a distinct interface exists across the divider. The transient mixing characteristic of the two fluids is addressed by following the Lagrangian history of the interface for various aspect ratios in the z-plane (depth variation) as well as a range of pulling velocities of the divider. The mixing characteristics of the two fluids are quantified from measurement of the length stretch of the interface and its flow field using respectively image processing techniques and Particle Imaging Velocimetry. Scaling analysis shows that the length stretch depends on four governing parameters, namely the Grashof number (Gr), Schmidt number (Sc), aspect ratio (Ar), and Reynolds number (Re). Variation of the Schmidt number is taken into account through thermophysical property variation. Thus our problem reduces to a codimension three bifurcation in parametric space for Gr, Ar, and Re. Our experimental results show that for Gr on the order of 106 and a nominal cavity aspect ratio Ar = 0.2, the net effect of removal of the divider and the overwhelming buoyancy force causes an overturning motion which stretches and folds the interface to produce ml internal breakwave. The structure of the breakwave is similar to the ubiquitous Rayleigh-Taylor instability morphology. The breakwave is dissipated either through internal or wall collision depending on the impulsive velocity of the divider as prescribed by the Reynolds number. The decay of the collision event occurs through sloshing oscillations over a short time scale. The two fluids then become stably stratified with a diffusive band at the interface indicating local mass transport. The local bifurcation of the internal breakwave is investigated as a function of aspect ratio. Results show that for narrow cavities on the order of 2mm (Ar = 0.04) folding does not occur, the interface only stretches. As the cavity size increases folding occurs through a supercritical bifurcation. Insight into the mechanism of folding is obtained from measurement of the flow field which shows that in the neighborhood of the folding event, there exists hyperbolic points caused by multiple vortex interactions. The global length stretch of the interface as a function of time is nearly Gaussian; calculations of finite-time Liapunov exponents as well as construction of horseshoe maps indicate the likelihood of a chaotic transient.

W.M.B. Duval↗

NASA NTRS2000

Stereo Imaging Velocimetry of Mixing Driven by Buoyancy Induced Flow Fields

Mixing of two fluids generated by steady and particularly g-jitter acceleration is fundamental towards the understanding of transport phenomena in a microgravity environment. We propose to carry out flight and ground-based experiments to quantify flow fields due to g-jitter type of accelerations using Stereo Imaging Velocimetry (SIV), and measure the concentration field using laser fluorescence. The understanding of the effects of g-jitter on transport phenomena is of great practical interest to the microgravity community and impacts the design of experiments for the Space Shuttle as well as the International Space Station. The aim of our proposed research is to provide quantitative data to the community on the effects of g-jitter on flow fields due to mixing induced by buoyancy forces. The fundamental phenomenon of mixing occurs in a broad range of materials processing encompassing the growth of opto-electronic materials and semiconductors, (by directional freezing and physical vapor transport), to solution and protein crystal growth. In materials processing of these systems, crystal homogeneity, which is affected by the solutal field distribution, is one of the major issues. The understanding of fluid mixing driven by buoyancy forces, besides its importance as a topic in fundamental science, can contribute towards the understanding of how solutal fields behave under various body forces. The body forces of interest are steady acceleration and g-jitter acceleration as in a Space Shuttle environment or the International Space Station. Since control of the body force is important, the flight experiment will be carried out on a tunable microgravity vibration isolation mount, which will permit us to precisely input the desired forcing function to simulate a range of body forces. To that end, we propose to design a flight experiment that can only be carried out under microgravity conditions to fully exploit the effects of various body forces on fluid mixing. Recent flight experiments, by the P.I. through collaboration with the Canadian Space Agency (STS-85, August 1997), aimed at determining the stability of the interface between two miscible liquids inside an enclosure show that a long liquid column (5 cm) under microgravity isolation conditions can be stable, i.e. the interface remains sharp and vertical over a short time scale; thus transport occurs by molecular mass diffusion. On the other hand, when the two liquids were excited from a controlled vibration source (Microgravity Vibration Isolation Mount) two to four mode large amplitude quasi-stationary waves were observed. The data was limited to CCD recording of the dynamics of the interface between the two fluids. We propose to carry out flight experiments to quantify the dynamics of the flow field using Stereo Imaging Velocimetry and measure the concentration field using laser fluorescence. The results will serve as a basis to understand effects of g-jitter on transport phenomena, in this case mass diffusion. As the measurement of the kinematics of the flow field will shed light on the instability mechanism. The research will allow measurement of the flow field in microgravity environment to prove two hypotheses: (1) Maxwell's hypothesis: finite convection always exists in diffusing systems, and (2) Quasi-stationary waves inside a bounded enclosure in a microgravity environment is generated by Kelvin-Helmholtz instability; resonance of the interface which produces incipient mixing is due to Rayleigh-Taylor instability. The first hypothesis can be used as a benchmark experiment to illustrate diffusive mixing. The second hypothesis will lead to the understanding of g-jitter effects on buoyancy driven flow fields which occur in many situations involving materials processing, and other basic fluid physics phenomena. In addition, the second hypothesis will also provide insight in how Rayleigh-Taylor and Kelvin-Helmholtz instabilities propagate concentration fronts during mixing. Measurement of the flow field using SIV is important because it is the flow field which causes instability at the interface between the two fluids. Mixing driven by buoyancy induced flow fields will be addressed both experimentally and computationally. The experimental effort will address the kinematics of mixing: stretching, transport and chaos. Quantification of the mechanisms of mixing will consists of measuring the flow field using the SIV system at Glenn and capturing the dynamics of the interface, to measure mass transport, using a CCD camera. These experiments will be carried out within the framework of Earth's gravity and g-jitter microgravity acceleration as in a Space Shuttle environment or the International Space Station. The g-jitter will be induced and controlled using a tunable vibration isolation platform to isolate against vibration as well as input periodic and random vibration to the system. The parametric range of the microgravity experiment will be extended from the experiments on STS-85 to investigate higher mode quasi-stationary waves (8 to 12), as well as resonance regions which leads to chaos and turbulence. Ground-based experiments will focus on effects of vibration on stably stratified fluid layers in order to scale for possible scenarios in a microgravity environment. These vibrations will be subjected perpendicular to the concentration field on the ground since the parallel case can only be carried out in a microgravity environment. The concept of dynamical similarity will be applied to tune the experiments as closely as possible to a Space Shuttle environment or the International Space Station. The computational effort will take advantage of the Computational Laboratory at Glenn to corroborate the experimental findings with predictions of the dynamics of the flow field using the codes FLUENT (finite difference based) and FIDAP (finite element based). We will investigate two important cases, single-fluid model to address dilute systems with negligible jump in viscosity and the more general two-fluid model which accounts for finite jump in viscosity. Apart from its microgravity relevance, this experiment is well suited to study dynamics in nonlinear systems.

Duval, W. M. B.↗

NASA NTRS1987

Performance and efficiency evaluation and heat release study of a direct-injection stratified-charge rotary engine

A computer simulation which models engine performance of the Direct Injection Stratified Charge (DISC) rotary engines was used to study the effect of variations in engine design and operating parameters on engine performance and efficiency of an Outboard Marine Corporation (OMC) experimental rotary combustion engine. Engine pressure data were used in a heat release analysis to study the effects of heat transfer, leakage, and crevice flows. Predicted engine data were compared with experimental test data over a range of engine speeds and loads. An examination of methods to improve the performance of the rotary engine using advanced heat engine concepts such as faster combustion, reduced leakage, and turbocharging is also presented.

Nguyen, H. L.↗

NASA NTRS1981

The Lagrangian-mean motions forced by steady, dissipating equatorial waves. I

Waves are treated with a normal mode structure in order to determine the steady mean motion of the atmosphere that can be induced by dissipating equatorial waves. A model is developed which comprises a continuously stratified atmosphere at rest on the equatorial beta-plane. It is assumed that waves are excited by the corrugated bottom and are in a steady state, that dissipation is due to Newtonian cooling and Rayleigh friction, steadiness in wave magnitude is up to the second order, the waves have a long wave length, wave induced mean flows do not affect the waves, mean flows are steady, and dissipation mechanisms for the mean flows are the same as for the waves. Disturbance equations are formulated, along with Eulerian- and Lagrangian-mean flows, and the nonexistence of cross equatorial mean flows is demonstrated. Kelvin waves are shown to possess a Lagrangian-mean meridional circulation which is the same as the Eulerian-mean circulation. In the Boussinesq limit, however, neither the Eulerian- nor the Lagrangian-mean meridional circulations are caused by Kelvin waves. Further examination is made of Rossby-gravity waves and n = 1 westward propagating inertio-gravity waves.

Takahashi, M.↗

NASA NTRS2011

Crater Flux Transfer Events: Highroad to the X Line?

We examine Cluster observations of a so-called magnetosphere crater FTE, employing data from five instruments (FGM, CIS, EDI, EFW, and WHISPER), some at the highest resolution. The aim of doing this is to deepen our understanding of the reconnection nature of these events by applying recent advances in the theory of collisionless reconnection and in detailed observational work. Our data support the hypothesis of a stratified structure with regions which we show to be spatial structures. We support the bulge-like topology of the core region (R3) made up of plasma jetting transverse to reconnected field lines. We document encounters with a magnetic separatrix as a thin layer embedded in the region (R2) just outside the bulge, where the speed of the protons flowing approximately parallel to the field maximizes: (1) short (fraction of a sec) bursts of enhanced electric field strengths (up to approximately 30 mV/m) and (2) electrons flowing against the field toward the X line at approximately the same time as the bursts of intense electric fields. R2 also contains a density decrease concomitant with an enhanced magnetic field strength. At its interface with the core region, R3, electric field activity ceases abruptly. The accelerated plasma flow profile has a catenary shape consisting of beams parallel to the field in R2 close to the R2/R3 boundary and slower jets moving across the magnetic field within the bulge region. We detail commonalities our observations of crater FTEs have with reconnection structures in other scenarios. We suggest that in view of these properties and their frequency of occurrence, crater FTEs are ideal places to study processes at the separatrices, key regions in magnetic reconnection. This is a good preparation for the MMS mission.

Farrugia, C. J.↗

NASA NTRS1986

Small-scale motions observed by aircraft in the tropical lower stratosphere - Evidence for mixing and its relationship to large-scale flows

Measurements of temperature and ozone from instrumented aircraft in the tropical lower stratosphere show the presence of small-scale disturbances generated by underlying cumulus convection and Kelvin-Helmholtz instability. The disturbances associated with underlying convection have peak-to-peak vertical parcel excursions of about 300 m. Flying conditions were smooth, suggesting an ensemble of gravity waves and little or no turbulent mixing. It is nevertheless possible that these waves break at other altitudes, leading to turbulent mixing and net fluxes of vertically stratified tracers. Disturbances attributed to KH instability implied vertical parcel excursions of 300-400 m. The disturbances coincided with rough flying conditions, suggesting turbulent mixing. A linear stability analysis of the atmospheric basic state defined by high-resolution radiosondes shows fastest growing waves with horizontal wavelengths of 1.4-1.8 km, consistent with the aircraft observations. The strong shears responsible for the KH instability are due to large-scale waves propagating into a region of small intrinsic frequency. Radiosonde observations show that the zonal length scale of these waves is about 1000 km.

Pfister, Leonhard↗

NASA NTRS1998

LSPRAY: Lagrangian Spray Solver for Applications With Parallel Computing and Unstructured Gas-Phase Flow Solvers

Sprays occur in a wide variety of industrial and power applications and in the processing of materials. A liquid spray is a phase flow with a gas as the continuous phase and a liquid as the dispersed phase (in the form of droplets or ligaments). Interactions between the two phases, which are coupled through exchanges of mass, momentum, and energy, can occur in different ways at different times and locations involving various thermal, mass, and fluid dynamic factors. An understanding of the flow, combustion, and thermal properties of a rapidly vaporizing spray requires careful modeling of the rate-controlling processes associated with the spray's turbulent transport, mixing, chemical kinetics, evaporation, and spreading rates, as well as other phenomena. In an attempt to advance the state-of-the-art in multidimensional numerical methods, we at the NASA Lewis Research Center extended our previous work on sprays to unstructured grids and parallel computing. LSPRAY, which was developed by M.S. Raju of Nyma, Inc., is designed to be massively parallel and could easily be coupled with any existing gas-phase flow and/or Monte Carlo probability density function (PDF) solver. The LSPRAY solver accommodates the use of an unstructured mesh with mixed triangular, quadrilateral, and/or tetrahedral elements in the gas-phase solvers. It is used specifically for fuel sprays within gas turbine combustors, but it has many other uses. The spray model used in LSPRAY provided favorable results when applied to stratified-charge rotary combustion (Wankel) engines and several other confined and unconfined spray flames. The source code will be available with the National Combustion Code (NCC) as a complete package.

Raju, Manthena S.↗

NASA NTRS2017

Flow Structure Comparison for Two 7-Point LDI Configurations

This paper presents a comparison primarily of the cold flow 2-D velocity profiles; and describes flame tube combusting flow operability for a 7-point Lean Direct Injector (LDI). This circular LDI array consists of a center element surrounded by six outer elements spaced 60 degrees apart; the spacing between all adjacent elements is the same. Each element consists of a simplex atomizer that injects at the throat of a converging-diverging venturi, and an axial swirler upstream of the venturi throat to generate swirl. The two configurations were: 1) one which consists of all 60 deg co-swirling axial air swirlers, and; 2) one configuration which uses a 60 deg swirler in the center, surrounded by counter-swirling 45 deg swirlers. Testing was done at 5- bar and at an inlet temperature of 700K. Two air reference velocities were considered in the cold flow measurements. The 2D velocity profiles were determined using particle image velocimetry. Results indicate the configuration using all 60 deg swirlers generates a field that moderates to a more uniform distribution at a shorter distance downstream and is more easily operable than the second configuration, which produces recirculation regions at the edges of the outer 45 deg swirlers, and results in a more stratified velocity field at any given axial location.

velocity↗

NASA NTRS2012

Upper-Ocean Heat Balance Processes and the Walker Circulation in CMIP5 Model Projections

Considerable uncertainty remains as to the importance of mechanisms governing decadal and longer variability of the Walker Circulation, its connection to the tropical climate system, and prospects for tropical climate change in the face of anthropogenic forcing. Most contemporary climate models suggest that in response to elevated CO2 and a warmer but more stratified atmosphere, the required upward mass flux in tropical convection will diminish along with the Walker component of the tropical mean circulation as well. Alternatively, there is also evidence to suggest that the shoaling and increased vertical stratification of the thermocline in the eastern Pacific will enable a muted SST increase there-- preserving or even enhancing some of the dynamical forcing for the Walker cell flow. Over the past decade there have been observational indications of an acceleration in near-surface easterlies, a strengthened Pacific zonal SST gradient, and globally-teleconnected dislocations in precipitation. But is this evidence in support of an ocean dynamical thermostat process posited to accompany anthropogenic forcing, or just residual decadal fluctuations associated with variations in warm and cold ENSO events and other stochastic forcing? From a modeling perspective we try to make headway on this question by examining zonal variations in surface energy fluxes and dynamics governing tropical upper ocean heat content evolution in the WCRP CMIP5 model projections. There is some diversity among model simulations; for example, the CCSM4 indicates net ocean warming over the IndoPacific region while the CSIRO model concentrates separate warming responses over the central Pacific and Indian Ocean regions. The models, as with observations, demonstrate strong local coupling between variations in column water vapor, downward surface longwave radiation and SST; but the spatial patterns of changes in the sign of this relationship differ among models and, for models as a whole, with observations. Our analysis focuses initially on probing the inter-model differences in energy fluxes / transports and Walker Circulation response to forcing. We then attempt to identify statistically the El Nino- / La Nina-related ocean heat content variability unique to each model and regress out the associated energy flux, ocean heat transport and Walker response on these shorter time scales for comparison to that of the anthropogenic signals.

Robertson, F. R.↗

NASA NTRS1992

The structure of the polar vortex

The paper develops a comparative picture of the 1987 Southern Hemisphere and 1989 Northern Hemisphere lower stratospheric, polar vortex circulation and constituent distributions as observed by the Airborne Antarctic Ozone Experiment, August 17-September 22, 1987, and Airborne Arctic Stratospheric Expedition, January 3-February 19, 1989 aircraft campaigns. Overall, both polar vortices define a region of highly isolated air, where the exchange of trace gases occurs principally at the vortex edge through erosional wave activity. Aircraft measurement showed that between 50 and 100 mbar, horizontally stratified long-lived tracers such as N2O are displaced downward 2-3 km on the cyclonic (poleward) side of the jet with the meridional tracer gradient sharpest at the jet core. Eddy mixing rates, computed using parcel ensemble statistics, are an order of magnitude or more lower on the cyclonic side of the jet compared to those on the anticyclonic side. Poleward zonal mean meridional flow on the anticyclonic side of the jet terminates in a descent zone at the jet core.

Schoeberl, Mark R.↗

NASA NTRS1993

Mixing and transient interface condensation of a liquid hydrogen tank

Experiments were conducted to investigate the effect of axial jet-induced mixing on the pressure reduction of a thermally stratified liquid hydrogen tank. The tank was nearly cylindrical, having a volume of about 0.144 cu m with 0.559 m in diameter and 0.711 m long. A mixer/pump unit, which had a jet nozzle outlet of 0.0221 m in diameter was located 0.178 m from the tank bottom and was installed inside the tank to generate the axial jet mixing and tank fluid circulation. The liquid fill and jet flow rate ranged from 42 to 85 percent (by volume) and 0.409 to 2.43 cu m/hr, respectively. Mixing tests began with the tank pressure ranging from 187.5 to 238.5 kPa at which the thermal stratification results in 4.9 to 6.2 K liquid sub cooling. The mixing time and transient vapor condensation rate at the liquid-vapor interface are determined. Two mixing time correlations, based on the thermal equilibrium and pressure equilibrium, are developed. Both mixing time correlations are expressed as functions of system and buoyancy parameters and compared well with other experimental data. The steady state condensation rate correlation of Sonin et al. based on steam-water data is modified and expressed as a function of jet subcooling. The limited liquid hydrogen data of the present study shows that the modified steady state condensation rate correlation may be used to predict the transient condensation rate in a mixing process if the instantaneous values of jet sub cooling and turbulence intensity at the interface are employed.

Lin, C. S.↗

NASA NTRS1972

Space-charge dynamics of liquids.

The propagation and instability characteristics of small-signal electro-fluid-mechanical space-charge and polarization waves in nonhomogeneous fluids are developed. Stratified equilibrium configurations with fluid properties and space-charge density constant within planar, cylindrical, and spherical surfaces, are emphasized. Equilibrium electric fields due both to charges in the fluid and to externally imposed potentials are normal to these surfaces. The liquid is modeled as incompressible, inviscid, and perfectly insulating, with domains of sufficiently high frequency or growth rate to validate the last assumption defined in terms of electrical conductivity or mobility. A general set of relations for perturbation field and flow variables on the perturbed surfaces of fluid layers having constant properties and space charge are derived in each of the configurations.

Zahn, M.↗

NASA NTRS2010

Packing Optimization of an Intentionally Stratified Sorbent Bed Containing Dissimilar Media Types

The Fire Cartridge is a packed bed air filter with two different and separate layers of media designed to provide respiratory protection from combustion products after a fire event on the International Space Station (ISS). The first layer of media is a carbon monoxide catalyst made from gold nanoparticles dispersed on iron oxide. The second layer of media is universal carbon, commonly used in commercial respirator filters. Each layer must be optimally packed to effectively remove contaminants from the air. Optimal packing is achieved by vibratory agitations. However, if post-packing movement of the media within the cartridge occurs, mixing of the bed layers, air voids, and channeling could cause preferential air flow and allow contaminants to pass. Several iterations of prototype fire cartridges were developed to reduce post-packing movement of the media within each layer (settling), and to prevent mixing of the two media types. Both types of movement of the media contribute to decreased fire cartridge performance. Each iteration of the fire cartridge design was tested to demonstrate mechanical loads required to cause detrimental movement within the bed, and resulting level of functionality of the media beds after movement was detected. In order to optimally pack each layer, vertical, horizontal, and orbital agitations were tested and a final packed bulk density was calculated for each method. Packed bulk density must be calculated for each lot of catalyst to accommodate variations in particle size, shape, and density. In addition, a physical divider sheet between each type of media was added within the fire cartridge design to further inhibit intermixing of the bed layers.

Kidd, Jessica↗

NASA NTRS1974

Linear viscous stability analysis of the stratified Bickley jet

The stability of the stably stratified Bickley jet to small disturbances in a viscous, heat conducting fluid is explored by numerical integration of the governing differential equation. Curves of neutral stability are presented in the alpha-R plane and the parametric dependence of these curves upon Richardson number and Prandtl number is examined. The results show a curious bimodal behavior of the curve of neutral stability for small Richardson numbers. In addition, closed neutral curves are found for Richardson numbers in excess of the critical value for the inviscid flow. The unstable regions in the interior of these curves increase with decreasing Prandtl number. Energy balances are computed which show the relative magnitude of the Reynolds stress production, buoyancy dissipation, and viscous dissipation terms across the flow. As the thermal diffusivity becomes large compared with the kinematic viscosity, the buoyancy term is suppressed and the thermal stratification becomes irrelevant.

Gage, K. S.↗

NASA NTRS2018

Parameterization of Mixed Layer and Deep-Ocean Mesoscales Including Nonlinearity

In 2011, Chelton et al. carried out a comprehensive census of mesoscales using altimetry data and reached the following conclusions: "essentially all of the observed mesoscale features are nonlinear" and "mesoscales do not move with the mean velocity but with their own drift velocity," which is "the most germane of all the nonlinear metrics." Accounting for these results in a mesoscale parameterization presents conceptual and practical challenges since linear analysis is no longer usable and one needs a model of nonlinearity. A mesoscale parameterization is presented that has the following features: 1) it is based on the solutions of the nonlinear mesoscale dynamical equations, 2) it describes arbitrary tracers, 3) it includes adiabatic (A) and diabatic (D) regimes, 4) the eddy-induced velocity is the sum of a Gent and McWilliams (GM) term plus a new term representing the difference between drift and mean velocities, 5) the new term lowers the transfer of mean potential energy to mesoscales, 6) the isopycnal slopes are not as flat as in the GM case, 7) deep-ocean stratification is enhanced compared to previous parameterizations where being more weakly stratified allowed a large heat uptake that is not observed, 8) the strength of the Deacon cell is reduced. The numerical results are from a stand-alone ocean code with Coordinated Ocean-Ice Reference Experiment I (CORE-I) normal-year forcing.

Baroclinic flows; Mesoscale processes; Mixing; Sub↗

NASA NTRS1977

Basalts from Mare Crisium

The stratified core sample returned from Mare Crisium by the Luna 24 unmanned space probe is composed primarily of a variety of subophitic to ophitic basalt with very low contents of TiO2 and MgO. This consists of clinopyroxene, calcic plagioclase, olivine, and minor amounts of silica, chromite, ulvoespinel, ilmenite, troilite, apatite, and Fe-metal. Granular metabasalts have the same bulk composition, but mineral phases exhibit less compositional variation. Fine-grained impact melts have similar compositions and are apparently derived from these basalts. It is concluded that the basalts, which are chemically distinct from the very-low-titanium basalts found elsewhere on the moon, represent the local surface flows of Mare Crisium. Sparse fragments of an olivine vitrophyre that is low in TiO2 but high in MgO and approaches the composition of the Apollo 15 green glasses may be derived from patches of dark mantling materials 20 km from the landing site.

Ryder, G.↗

NASA NTRS1980

The heating of a thermally conducting stratified medium. I - Self-gravitating gas threaded by magnetic fields

Two theoretical problems are presented to illustrate the equilibrium structure of a gravitating gas threaded by magnetic fields. The gas is heated everywhere at a rate proportional to the local density and cooled by thermal conduction channeled along the magnetic field. Emphasis is placed on the influence of anisotropic thermal conduction on the distribution of the gas. In the first problem, the magnetic field has straight field lines that are nearly parallel. The simple field line geometry allows us to calculate, in closed form, the equilibria configurations of a gas slab which is cooled nonuniformly by thermal conduction along field lines which leave the gas slab at varying angles. The problem involves the gas having a free boundary, which is one of the unknowns to be determined. A discussion is given of the set of all possible equilibria so constructed. In the second problem there is no electric current flowing in the gas but there is a potential magnetic field having curved field lines. Exact solutions of equilibriums are presented to illustrate the heating of stellar and galactic coronas.

Lerche, I.↗