Formation of jets by implusive acceleration of a curved free surface

The sudden axial acceleration of a column of liquid bounded at one end by a concave free surface has been found, experimentally, to produce a jet which issues from the free surface with a speed several times that imparted to the column.

Theoretical approximations to such flows, valid for small time, are formulated subject to the assumption that the fluid is inviscid and incompressible. In a special two-dimensional case, it is found that, for vanishingly small time, the velocity at the point on the free surface from which the jet emanates is π/2 times the velocity imparted to the column. The solutions to several problems in two and three dimensions assuming that the initial curvature of the free surface is small, lead to values for this ratio dependent upon the curvature—the initial velocity in the case of axial symmetry exceeding that of the analogous two-dimensional problem by approximately 25%.

Experiments conducted upon the phenomenon give values systematically in excess of those predicted by the theory, although theory and experiment are in qualitative agreement with respect to the displacement of the free surface. It is suggested that the discrepancy is attributable to effects of finite curvature having been imperfectly accounted for in the axially-symmetric analysis.

Photographic materials on pp. 115, 120, and 121 are essential and will not reproduce clearly on Xerox copies. Photographic copies should be ordered.

The streaming of 1.3-2.3 MeV cosmic-ray protons during periods between prompt solar particle events

The anisotropy of 1.3 - 2.3 MeV protons in interplanetary space has been measured using the Caltech Electron/Isotope Spectrometer aboard IMP-7 for 317 6-hour periods from 72/273 to 74/2. Periods dominated by prompt solar particle events are not included. The convective and diffusive anisotropies are determined from the observed anisotropy using concurrent solar wind speed measurements and observed energy spectra. The diffusive flow of particles is found to be typically toward the sun, indicating a positive radial gradient in the particle density. This anisotropy is inconsistent with previously proposed sources of low-energy proton increases seen at 1 AU which involve continual solar acceleration.

The typical properties of this new component of low-energy cosmic rays have been determine d for this period which is near solar minimum. The particles have a median intensity of 0.06 protons/ cm^(2)-sec-sr-MeV and a mean spectral index of -3.15.The amplitude of the diffusive anisotropy is approximately proportional to the solar wind speed. The rate at which particles are diffusing toward the sun is larger than the rate at which the solar wind is convecting the particles away from the sun. The 20 to 1 proton to alpha ratio typical of this new component has been reported by Mewaldt, et al. (1975b).

A propagation model with κ_(rr) assumed independent of radius and energy is used to show that the anisotropy could be due to increases similar to those found by McDonald, et al. (1975) at ~3 AU. The interplanetary Fermi-acceleration model proposed by Fisk (1976) to explain the increases seen near 3 AU is not consistent with the ~12 per cent diffusive anisotropy found.

The dependence of the diffusive anisotropy on various parameters is shown. A strong dependence of the direction of the diffusive anisotropy on the concurrently measured magnetic field direction is found, indicating a κ_⊥ less than κ_∥ to be typical for this large data set.

On the settling speed of dilute arrays of spheres

A method is developed to calculate the settling speed of dilute arrays of spheres for the three cases of: I, a random array of freely moving particles; II, a random array of rigidly held particles; and III, a cubic array of particles. The basic idea of the technique is to give a formal representation for the solution and then manipulate this representation in a straightforward manner to obtain the result. For infinite arrays of spheres, our results agree with the results previously found by other authors, and the analysis here appears to be simpler. This method is able to obtain more terms in the answer than was possible by Saffman's unified treatment for point particles. Some results for arbitrary two sphere distributions are presented, and an analysis of the wall effect for particles settling in a tube is given. It is expected that the method presented here can be generalized to solve other types of problems.

The distribution and ages of regional lithologies in the lunar maria

A research program was designed (1) to map regional lithological units of the lunar surface based on measurements of spatial variations in spectral reflectance, and, (2) to establish the sequence of the formation of such lithological units from measurements of the accumulated affects of impacting bodies.

Spectral reflectance data were obtained by scanning luminance variations over the lunar surface at three wavelengths (0.4µ, 0.52µ, and 0.7µ). These luminance measurements were reduced to normalized spectral reflectance values relative to a standard area in More Serenitotis. The spectral type of each lunar area was identified from the shape of its reflectance spectrum. From these data lithological units or regions of constant color were identified. The maria fall into two major spectral classes: circular moria like More Serenitotis contain S-type or red material and thin, irregular, expansive maria like Mare Tranquillitatis contain T-type or blue material. Four distinct subtypes of S-type reflectances and two of T-type reflectances exist. As these six subtypes occur in a number of lunar regions, it is concluded that they represent specific types of material rather than some homologous set of a few end members.

The relative ages or sequence of formation of these more units were established from measurements of the accumulated impacts which have occurred since more formation. A model was developed which relates the integrated flux of particles which hove impacted a surface to the distribution of craters as functions of size and shape. Erosion of craters is caused chiefly by small bodies which produce negligible individual changes in crater shape. Hence the shape of a crater can be used to estimate the total number of small impacts that have occurred since the crater was formed. Relative ages of a surface can then be obtained from measurements of the slopes of the walls of the oldest craters formed on the surface. The results show that different maria and regions within them were emplaced at different times. An approximate absolute time scale was derived from Apollo 11 crystallization ages under an assumption of a constant rote of impacting for the last 4 x 10^9 yrs. Assuming, constant flux, the period of mare formation lasted from over 4 x 10^9 yrs to about 1.5 x 10^9 yrs ago.

A synthesis of the results of relative age measurements and of spectral reflectance mapping shows that (1) the formation of the lunar maria occurred in three stages; material of only one spectral type was deposited in each stage, (2) two distinct kinds of maria exist, each type distinguished by morphology, structure, gravity anomalies, time of formation, and spectral reflectance type, and (3) individual maria have complicated histories; they contain a variety of lithic units emplaced at different times.

Solar photospheric and coronal abundances from solar energetic particle measurements

Observations of solar energetic particles (SEPs) from 22 solar flares in the 1977-1982 time period are reported. The observations were made by the Cosmic Ray Subsystem on board the Voyager 1 and 2 spacecraft. SEP abundances have been obtained for all elements with 3 ≤ Z ≤ 30 except Li, Be, B. F, Sc, V, Co and Cu. for which upper limits have been obtained. Statistically meaningful abundances of several rare elements (e.g., P, Cl, K, Ti, Mn) have been determined for the first time, and the average abundances of the more abundant elements have been determined with improved precision, typically a factor of three better than the best previous determinations.

Previously reported results concerning the dependence of the fractionation of SEPs relative to photosphere on first ionization potential (FIP) have been confirmed and amplified upon with the new data. The monotonic Z-dependence of the variation between flares noted by earlier studies was found to be interpretable as a fractionation, produced by acceleration of the particles from the corona and their propagation through interplanetary space, which is ordered by the ionic charge-to-mass ratio Q/ M of the species making up the SEPs. It was found that Q/M is the primary organizing parameter of acceleration and propagation effects in SEPs, as evidenced by the dependence on Q/M of time, spatial and energy dependence within flares and of the abundance variability from flare to flare.

An unfractionated coronal composition was derived by applying a simple Q/M fractionation correction to the observed average SEP composition, to simultaneously correct for all Q/M-correlated acceleration/propagation fractionation of SEPs. The resulting coronal composition agrees well with current XUV/X-ray spectroscopic measurements of coronal composition but is of much higher precision and is available for a much larger set of elements. Compared to spectroscopic photospheric abundances, the SEP-derived corona appears depleted in C and somewhat enriched in Cr (and possibly Ca and Ti).

An unfractionated photospheric composition was derived by applying a simple FIP fractionation correction to the derived coronal composition, to correct for the FIP-associated fractionation of the corona during its formation from photospheric material. The resulting composition agrees well with the photospheric abundance tabulation of Grevesse (1984) except for an at least 50% lower abundance of C and a significantly greater abundance of Cr and possibly Ti. The results support the Grevesse photospheric Fe abundance, about 50% higher than meteoritic and earlier solar values. The SEP-derived photospheric composition is not generally of higher precision than the available spectroscopic data, but it relies on fewer physical parameters and is available for some elements (C, N, Ne, Ar) which cannot be measured spectroscopically in the photosphere.

The abundances of ultraheavy elements in the cosmic radiation

Analysis of the data from the Heavy Nuclei Experiment on the HEAO-3 spacecraft has yielded the cosmic ray abundances of odd-even element pairs with atomic number, Z, in the range 33 ≤ Z ≤60, and the abundances of broad element groups in the range 62 ≤ Z ≤83, relative to iron. These data show that the cosmic ray source composition in this charge range is quite similar to that of the solar system provided an allowance is made for a source fractionation based on first ionization potential. The observations are inconsistent with a source composition which is dominated by either r-process or s-process material, whether or not an allowance is made for first ionization potential. Although the observations do not exclude a source containing the same mixture of r- and s-process material as in the solar system. the data are best fit by a source having an r- to s-process ratio of 1.22^(+0.25)_(0.21), relative to the solar system The abundances of secondary elements are consistent with the leaky box model of galactic propagation, implying a pathlength distribution similar to that which explains the abundances of nuclei with Z<29.

The energy spectra of the even elements in the range 38 ≤ Z ≤ 60 are found to have a deficiency of particles in the range ~1.5 to 3 GeV/amu, compared to iron. This deficiency may result from ionization energy loss in the interstellar medium, and is not predicted by propagation models which ignore such losses. ln addition, the energy spectra of secondary elements are found to be different to those of the primary elements. Such effects are consistent with observations of lighter nuclei, and are in qualitative agreement with galactic propagation models using a rigidity dependent escape length. The energy spectra of secondaries arising from the platinum group are found to be much steeper than those of lower Z. This effect may result from energy dependent fragmentation cross sections.

Investigation of Fundamental Processes Governing Secondary Organic Aerosol Formation in Laboratory Chambers

Our understanding of the processes and mechanisms by which secondary organic aerosol (SOA) is formed is derived from laboratory chamber studies. In the atmosphere, SOA formation is primarily driven by progressive photooxidation of SOA precursors, coupled with their gas-particle partitioning. In the chamber environment, SOA-forming vapors undergo multiple chemical and physical processes that involve production and removal via gas-phase reactions; partitioning onto suspended particles vs. particles deposited on the chamber wall; and direct deposition on the chamber wall. The main focus of this dissertation is to characterize the interactions of organic vapors with suspended particles and the chamber wall and explore how these intertwined processes in laboratory chambers govern SOA formation and evolution.

A Functional Group Oxidation Model (FGOM) that represents SOA formation and evolution in terms of the competition between functionalization and fragmentation, the extent of oxygen atom addition, and the change of volatility, is developed. The FGOM contains a set of parameters that are to be determined by fitting of the model to laboratory chamber data. The sensitivity of the model prediction to variation of the adjustable parameters allows one to assess the relative importance of various pathways involved in SOA formation.

A critical aspect of the environmental chamber is the presence of the wall, which can induce deposition of SOA-forming vapors and promote heterogeneous reactions. An experimental protocol and model framework are first developed to constrain the vapor-wall interactions. By optimal fitting the model predictions to the observed wall-induced decay profiles of 25 oxidized organic compounds, the dominant parameter governing the extent of wall deposition of a compound is identified, i.e., wall accommodation coefficient. By correlating this parameter with the molecular properties of a compound via its volatility, the wall-induced deposition rate of an organic compound can be predicted based on its carbon and oxygen numbers in the molecule.

Heterogeneous transformation of δ-hydroxycarbonyl, a major first-generation product from long-chain alkane photochemistry, is observed on the surface of particles and walls. The uniqueness of this reaction scheme is the production of substituted dihydrofuran, which is highly reactive towards ozone, OH, and NO3, thereby opening a reaction pathway that is not usually accessible to alkanes. A spectrum of highly-oxygenated products with carboxylic acid, ester, and ether functional groups is produced from the substituted dihydrofuran chemistry, thereby affecting the average oxidation state of the alkane-derived SOA.

The vapor wall loss correction is applied to several chamber-derived SOA systems generated from both anthropogenic and biogenic sources. Experimental and modeling approaches are employed to constrain the partitioning behavior of SOA-forming vapors onto suspended particles vs. chamber walls. It is demonstrated that deposition of SOA-forming vapors to the chamber wall during photooxidation experiments can lead to substantial and systematic underestimation of SOA. Therefore, it is likely that a lack of proper accounting for vapor wall losses that suppress chamber-derived SOA yields contribute substantially to the underprediction of ambient SOA concentrations in atmospheric models.

Experimental, Numerical and Analytical Studies of the MHD-driven plasma jet, instabilities and waves

This thesis describes a series of experimental, numerical, and analytical studies involving the Caltech magnetohydrodynamically (MHD)-driven plasma jet experiment. The plasma jet is created via a capacitor discharge that powers a magnetized coaxial planar electrodes system. The jet is collimated and accelerated by the MHD forces.

We present three-dimensional ideal MHD finite-volume simulations of the plasma jet experiment using an astrophysical magnetic tower as the baseline model. A compact magnetic energy/helicity injection is exploited in the simulation analogous to both the experiment and to astrophysical situations. Detailed analysis provides a comprehensive description of the interplay of magnetic force, pressure, and flow effects. We delineate both the jet structure and the transition process that converts the injected magnetic energy to other forms.

When the experimental jet is sufficiently long, it undergoes a global kink instability and then a secondary local Rayleigh-Taylor instability caused by lateral acceleration of the kink instability. We present an MHD theory of the Rayleigh-Taylor instability on the cylindrical surface of a plasma flux rope in the presence of a lateral external gravity. The Rayleigh-Taylor instability is found to couple to the classic current-driven instability, resulting in a new type of hybrid instability. The coupled instability, produced by combination of helical magnetic field, curvature of the cylindrical geometry, and lateral gravity, is fundamentally different from the classic magnetic Rayleigh-Taylor instability occurring at a two-dimensional planar interface.

In the experiment, this instability cascade from macro-scale to micro-scale eventually leads to the failure of MHD. When the Rayleigh-Taylor instability becomes nonlinear, it compresses and pinches the plasma jet to a scale smaller than the ion skin depth and triggers a fast magnetic reconnection. We built a specially designed high-speed 3D magnetic probe and successfully detected the high frequency magnetic fluctuations of broadband whistler waves associated with the fast reconnection. The magnetic fluctuations exhibit power-law spectra. The magnetic components of single-frequency whistler waves are found to be circularly polarized regardless of the angle between the wave propagation direction and the background magnetic field.

A molecular dynamics study of the microscopic properties of simple dense fluids

The microscopic properties of a two-dimensional model dense fluid of Lennard-Jones disks have been studied using the so-called "molecular dynamics" method. Analyses of the computer-generated simulation data in terms of "conventional" thermodynamic and distribution functions verify the physical validity of the model and the simulation technique.

The radial distribution functions g(r) computed from the simulation data exhibit several subsidiary features rather similar to those appearing in some of the g(r) functions obtained by X-ray and thermal neutron diffraction measurements on real simple liquids. In the case of the model fluid, these "anomalous" features are thought to reflect the existence of two or more alternative configurations for local ordering.

Graphical display techniques have been used extensively to provide some intuitive insight into the various microscopic phenomena occurring in the model. For example, "snapshots" of the instantaneous system configurations for different times show that the "excess" area allotted to the fluid is collected into relatively large, irregular, and surprisingly persistent "holes". Plots of the particle trajectories over intervals of 2.0 to 6.0 x 10^-12 sec indicate that the mechanism for diffusion in the dense model fluid is "cooperative" in nature, and that extensive diffusive migration is generally restricted to groups of particles in the vicinity of a hole.

A quantitative analysis of diffusion in the model fluid shows that the cooperative mechanism is not inconsistent with the statistical predictions of existing theories of singlet, or self-diffusion in liquids. The relative diffusion of proximate particles is, however, found to be retarded by short-range dynamic correlations associated with the cooperative mechanism--a result of some importance from the standpoint of bimolecular reaction kinetics in solution.

A new, semi-empirical treatment for relative diffusion in liquids is developed, and is shown to reproduce the relative diffusion phenomena observed in the model fluid quite accurately. When incorporated into the standard Smoluchowski theory of diffusion-controlled reaction kinetics, the more exact treatment of relative diffusion is found to lower the predicted rate of reaction appreciably.

Finally, an entirely new approach to an understanding of the liquid state is suggested. Our experience in dealing with the simulation data--and especially, graphical displays of the simulation data--has led us to conclude that many of the more frustrating scientific problems involving the liquid state would be simplified considerably, were it possible to describe the microscopic structures characteristic of liquids in a concise and precise manner. To this end, we propose that the development of a formal language of partially-ordered structures be investigated.

Development of roll waves in open channels

This study is concerned with some of the properties of roll waves that develop naturally from a turbulent uniform flow in a wide rectangular channel on a constant steep slope . The wave properties considered were depth at the wave crest, depth at the wave trough, wave period, and wave velocity . The primary focus was on the mean values and standard deviations of the crest depths and wave periods at a given station and how these quantities varied with distance along the channel.

The wave properties were measured in a laboratory channel in which roll waves developed naturally from a uniform flow . The Froude number F (F = u_n/√gh_n, u_n = normal velocity , h_n = normal depth, g =acceleration of gravity) ranged from 3. 4 to 6. 0 for channel slopes S_o of . 05 and . 12 respectively . In the initial phase of their development the roll waves appeared as small amplitude waves with a continuous water surface profile . These small amplitude waves subsequently developed into large amplitude shock waves. Shock waves were found to overtake and combine with other shock waves with the result that the crest depth of the combined wave was larger than the crest depths before the overtake. Once roll waves began to develop, the mean value of the crest depths h_nmax increased with distance . Once the shock waves began to overtake, the mean wave period T_av increased approximately linearly with distance.

For a given Froude number and channel slope the observed quantities h^-_max/h_n , T' (T' = S_o T_av √g/h_n), and the standard deviations of h^-_max/h_n and T', could be expressed as unique functions of l/h_n (l = distance from beginning of channel) for the two-fold change in h_n occurring in the observed flows . A given value of h^-_max/h_n occurred at smaller values of l/h_n as the Froude number was increased. For a given value of h /hh^-_max/h_n the growth rate of δh^-_max/h^-_maxδl of the shock waves increased as the Froude number was increased.

A laboratory channel was also used to measure the wave properties of periodic permanent roll waves. For a given Froude number and channel slope the h^-_max/h_n vs. T' relation did not agree with a theory in which the weight of the shock front was neglected. After the theory was modified to include this weight, the observed values of h^-_max/h_n were within an average of 6.5 percent of the predicted values, and the maximum discrepancy was 13.5 percent.

For h^-_max/h_n sufficiently large (h^-_max/h_n > approximately 1.5) it was found that the h^-_max/h_n vs. T' relation for natural roll waves was practically identical to the h^-_max/h_n vs. T' relation for periodic permanent roll waves at the same Froude number and slope. As a result of this correspondence between periodic and natural roll waves, the growth rate δh^-_max/h^-_maxδl of shock waves was predicted to depend on the channel slope, and this slope dependence was observed in the experiments.

Experimental study study of antiproton-proton annihilation into a pair of charged Pi-Mesons or K-Mesons for incident antiproton mementa in the range from 0.72 GeV/c to 2.62 GeV/c

The cross sections for the two antiproton-proton annihilation-in-flight modes,

ˉp + p → π⁺ + π^-

ˉp + p → k⁺ + k^-

were measured for fifteen laboratory antiproton beam momenta ranging from 0.72 to 2.62 GeV/c. No magnets were used to determine the charges in the final state. As a result, the angular distributions were obtained in the form [dσ/dΩ (Θ_C.M.) + dσ/dΩ (π – Θ_C.M.)] for 45 ≲ Θ_C.M. ≲ 135°.

A hodoscope-counter system was used to discriminate against events with final states having more than two particles and antiproton-proton elastic scattering events. One spark chamber was used to record the track of each of the two charged final particles. A total of about 40,000 pictures were taken. The events were analyzed by measuring the laboratory angle of the track in each chamber. The value of the square of the mass of the final particles was calculated for each event assuming the reaction

ˉp + p → a pair of particles with equal masses.

About 20,000 events were found to be either annihilation into π ^±-pair or k ^±-pair events. The two different charged meson pair modes were also distinctly separated.

The average differential cross section of ˉp + p → π⁺ + π^- varied from ~ 25 µb/sr at antiproton beam momentum 0.72 GeV/c (total energy in center-of-mass system, √s = 2.0 GeV) to ~ 2 µb/sr at beam momentum 2.62 GeV/c (√s = 2.64 GeV). The most striking feature in the angular distribution was a peak at Θ_C.M. = 90° (cos Θ_C.M. = 0) which increased with √s and reached a maximum at √s ~ 2.1 GeV (beam momentum ~ 1.1 GeV/c). Then it diminished and seemed to disappear completely at √s ~ 2.5 GeV (beam momentum ~ 2.13 GeV/c). A valley in the angular distribution occurred at cos Θ_C.M. ≈ 0.4. The differential cross section then increased as cos Θ_C.M. approached 1.

The average differential cross section for ˉp + p → k⁺ + k^- was about one third of that of the π^±-pair mode throughout the energy range of this experiment. At the lower energies, the angular distribution, unlike that of the π^±-pair mode, was quite isotropic. However, a peak at Θ_C.M. = 90° seemed to develop at √s ~ 2.37 GeV (antiproton beam momentum ~ 1.82 GeV/c). No observable change was seen at that energy in the π^±-pair cross section.

The possible connection of these features with the observed meson resonances at 2.2 GeV and 2.38 GeV, and its implications, were discussed.

Thermodynamic and kinetic behavior of an argon plasma jet. Decomposition of nitric oxide between 1300 - 1750 degrees K in an argon plasma

In the first part of the study, an RF coupled, atmospheric pressure, laminar plasma jet of argon was investigated for thermodynamic equilibrium and some rate processes.

Improved values of transition probabilities for 17 lines of argon I were developed from known values for 7 lines. The effect of inhomogeneity of the source was pointed out.

The temperatures, T, and the electron densities, n_e , were determined spectroscopically from the population densities of the higher excited states assuming the Saha-Boltzmann relationship to be valid for these states. The axial velocities, v_z, were measured by tracing the paths of particles of boron nitride using a three-dimentional mapping technique. The above quantities varied in the following ranges: 10¹² ˂ n_e ˂ 10¹⁵ particles/cm³, 3500 ˂ T ˂ 11000 °K, and 200 ˂ v_z ˂ 1200 cm/sec.

The absence of excitation equilibrium for the lower excitation population including the ground state under certain conditions of T and n_e was established and the departure from equilibrium was examined quantitatively. The ground state was shown to be highly underpopulated for the decaying plasma.

Rates of recombination between electrons and ions were obtained by solving the steady-state equation of continuity for electrons. The observed rates were consistent with a dissociative-molecular ion mechanism with a steady-state assumption for the molecular ions.

In the second part of the study, decomposition of NO was studied in the plasma at lower temperatures. The mole fractions of NO denoted by x_NO were determined gas-chromatographically and varied between 0.0012 ˂ x_NO ˂ 0.0055. The temperatures were measured pyrometrically and varied between 1300 ˂ T ˂ 1750°K. The observed rates of decomposition were orders of magnitude greater than those obtained by the previous workers under purely thermal reaction conditions. The overall activation energy was about 9 kcal/g mol which was considerably lower than the value under thermal conditions. The effect of excess nitrogen was to reduce the rate of decomposition of NO and to increase the order of the reaction with respect to NO from 1.33 to 1.85. The observed rates were consistent with a chain mechanism in which atomic nitrogen and oxygen act as chain carriers. The increased rates of decomposition and the reduced activation energy in the presence of the plasma could be explained on the basis of the observed large amount of atomic nitrogen which was probably formed as the result of reactions between excited atoms and ions of argon and the molecular nitrogen.