A simplified stratified lake model for determining effects of wind variation and eddy diffusivity
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Vibrations of the National Transonic Facility model support system were analyzed using Computational Aeroelasticity Program-Transonic Small Disturbance, a three-dimensional transonic small disturbance code designed for aeroelastic analysis of complete aircraft. The model support system was represented as a tunnel-spanning flexible wing whose structural properties were obtained from measured responses. Aeroelastic transients were calculated and analyzed to obtain modal stability characteristics. The results show that there is tendency to exhibit a hump mode instability in one of the modes, and that there are other weakly damped or unstable modes. Most of the motion is in the aft section of the model support system. The close proximity of the solid wind-tunnel diffuser side walls to the model support system is shown to have adverse effects on its aeroelastic stability characteristics. When the effects of the wind-tunnel walls are modeled, the analyses indicate the presence of wind-tunnel resonance modes which are not present when free-air boundary conditions are used.
A model for electron and proton energy and density in Jupiter's radiation belt is proposed. It is assumed that electrons diffuse inward from the solar wind. The Davis and Chang diffusion model, in which there is a very steep L-shell dependence in density and energy, is scaled outwards from the peak of the belts at about 1.5 to 2 Jupiter radii to the magnetopause as defined by the magnetic moment. The energetic electron density is calculated to be one billionth of the density in the solar wind, and that is assumed to be the trapping ratio of Jupiter's synchrotron belts. It is further assumed that the same figures apply to protons. The flux density at 80 MHz was measured by the Culgoora ring to be identical to that at 3000 MHz, implying a constant flux density of the synchrotron source of over 20 or 30 to 1 in frequency. It is suggested that the synchrotron spectrum is flat over more than an order of magnitude of frequency. Jupiter is an enormous synchrotron source and has a strong magnetic field, causing long diffusion times for electrons in the magnetosphere.
The topology of lunar remanent fields is investigated by analyzing simultaneous magnetometer and solar wind spectrometer data. The diffusion model proposed by Vanyan (1977) to describe the field-plasma interaction at the lunar surface is extended to describe the interaction with fields characterized by two scale lengths, and the extended model is compared with data from three Apollo landing sites (Apollo 12, 15 and 16) with crustal fields of differing intensity and topology. Local remanent field properties from this analysis are compared with high spatial resolution magnetic maps obtained from the electron reflection experiment. It is concluded that remanent fields over most of the lunar surface are characterized by spatial variations as small as a few kilometers. Large regions (50 to 100 km) of the lunar crust were probably uniformly magnetized early in the evolution of the crust. Smaller scale (5 to 10 km) magnetic sources close to the surface were left by bombardment and subsequent gardening of the upper layers of these magnetized regions. The small scale sized remanent fields of about 100 gammas are measured by surface experiments, whereas the larger scale sized fields of about 0.1 gammas are measured by the orbiting subsatellite experiments.
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A two-dimensional model of odd nitrogen in the thermosphere and upper mesosphere is described. The global distributions of nitric oxide and atomic nitrogen are calculated for the solstice period for quiet and moderate magnetic activity during the solar minimum period. The effect of thermospheric transport by winds is investigated along with the importance of particle-induced ionization in the auroral zones. The results are compared with rocket and satellite measurements, and the sensitivity of the model to eddy diffusion and neutral winds is investigated. Downward fluxes of NO into the mesosphere are given, and their importance for stratospheric ozone is discussed. The results show that the summer-to-winter pole meridional circulation transports both NO and N(S-4) across the solar terminator into the polar night region where there is a downward vertical transport toward the mesosphere. The model shows that odd nitrogen densities at high winter latitudes are entirely controlled by particle precipitation and transport processes.
The first results are presented from a series of computer simulations of the solar modulation of galactic cosmic rays using a full three-dimensional model which incorporates all known important effects on particle transport, particle drifts, convection with the solar wind, energy loss, and anisotropic diffusion. The model is time-independent in the coordinate frame rotating with the sun, so corotating effects can be studied. Modulation in an interplanetary magnetic field model is considered in which the current sheet separating the northern and southern solar hemispheres is warped and corotating with the sun. The amplitude of the warp is varied to simulate possible solar cycle variation of the magnetic field. Substantial effects due to the warp of the current sheet are found. Comparison of the model results with various data is presented. Among other things, it is shown that the intensity may decrease away from the current sheet for both signs of the magnetic field, as suggested by recent observations, and in contrast with inferences from earlier, more approximate calculations.
Variation in the eddy diffusion coefficient constitutes a momentum source. This variation near the turbopause affects both the composition and the wind and temperature fields of the thermosphere. Two types of calculations are carried out, for horizontal winds considered self-consistently in a three-dimensional dynamic model and horizontal winds artificially suppressed to simulate a one-dimensional model. Momentum transfer associated with variations in eddy diffusion coefficients represents the source function in the analysis presented. It is shown that for long-term variations in the thermosphere, the compositional dependence on variations in eddy diffusion coefficients can be entirely different in one and three dimensional models with horizontal winds included. Horizontal winds can greatly reduce the effects of eddy diffusion in general and the ratio between He and O amplitudes in particular.
A comparison is made between recent AMPTE/IRM observations of diffuse ions detected upstream of the earth's bow shock when the interplanetary magnetic field was nearly parallel to the solar wind direction and a known collisionless quasi-parallel shock model. These observations, which provide the proton spectrum for all of velocity space, give a direct measure of the shock acceleration efficiency and show how thermal solar winds are injected into the diffusive shock acceleration mechanism. The model accurately describes the proton spectrum; moreover, it predicts the shock structure, the complete particle spectrum, the relative velocity distributions of different ion species in the down stream region, and the enhancement of heavy ions over protons relative to the unshocked solar wind.
The mixing and transport of cosmic rays accelerated by a pulsar inside an expanding supernova remnant are examined, and the resulting high-energy gamma-ray emission from nuclear interactions of these accelerated particles in the shell is investigated. Rayleigh-Taylor instability at the interface between a pulsar wind cavity and the inner supernova envelope is assumed to be the mixing mechanism. The analysis is applied to the model of Gaisser, Harding, and Stanev (1987), where protons are accelerated at the reverse shock in the pulsar wind. The instability time-scale is estimated from the dynamics of the pulsar wind cavity, and model the injection, diffusion, and interaction of protons in the shell. The resulting gamma-ray flux is lower than previous estimates due to proton adiabatic losses in the expanding pulsar wind. The protons mix and diffuse only into the innermost regions of the envelope before interacting. Energy-dependent diffusion causes the higher energy gamma-ray light curves to decay faster than those at lower energy.
A steady-state model of Jupiter's electron radiation belt is developed. The model includes injection from the solar wind, radial diffusion, energy degradation by synchrotron radiation, and absorption at Jupiter's surface. A diffusion coefficient of the form D sub RR/R sub J squared = k times R to the m-th power is assumed, and then observed data on synchrotron radiation are used to fit the model. The free parameters determined from this fit are m = 1.95 plus or minus 0.5, k = 1.7 plus or minus 0.5 x 10 to the 9th power per sec, and the magnetic moment of injected particles equals 770 plus or minus 300 MeV/G. The value of m shows quite clearly that the diffusion is not caused by magnetic pumping by a variable solar wind or by a fluctuating convection electric field. The process might be field line exchange driven by atmospheric-ionospheric winds; our diffusion coefficient has roughly the same radial dependence but is considerably smaller in magnitude than the upper bound diffusion coefficients recently suggested for this process by Brice and McDonough (1973) and Jacques and Davis (1972).
Vibrations of the National Transonic Facility model support system were analyzed using CAP-TSD (Computational Aeroelasticity Program-Transonic Small Disturbance), a three-dimensional transonic small disturbance potential code designed for aeroelastic analysis of complex configurations. The model support system was represented as a tunnel-spanning flexible wing whose structural properties were obtained from measured responses. Aeroelastic transients were calculated, assuming no structural damping, and analyzed to obtain modal stability characteristics. The results showed that there is a tendency toward a hump mode instability in one of the modes and that there are other weakly damped or unstable modes. The close proximity of the solid wind-tunnel diffuser side walls to the model support system was shown to have adverse effects on its aeroelastic stability characteristics. When the effects of the wind-tunnel walls were modeled, the analyses indicated the presence of wind-tunnel resonance modes which were not present when free-air boundary conditions were used.
A simple model of the earth's bow shock is presented and compared with ISEE-1 observations of diffuse ions upstream of the shock. Ion behavior is modeled in a test particle simulation using Monte Carlo techniques for a plane parallel shock at which cold solar wind ions are heated sufficiently to allow diffusion back upstream. Fitting of the model to the observations indicates that the diffusion coefficient must increase faster than linearly with velocity, and provides an upper limit to the acceleration efficiency defined as the proportion of incoming solar wind ions accelerated and observed upstream. Results suggest that astrophysical shocks are capable of accelerating ions directly from the thermal plasma without the need for a distinct preenergizing injection stage.
A semi-empirical model based on a Gaussian vorticity distribution was developed for determining eddy diffusivity and wind transport distributions in the polar stratosphere. The model uses as input data pressure surface heights measured at periods of the year when the stratospheric polar vortex exhibits nearly circular patterns around the pole. The components of the polar wind velocities that result from a Prandtl eddy viscosity distribution are found to be in general agreement with those obtained by other investigators.
The 1-1/2-D model of Holton (1986), which is actually a highly truncated two-dimensional model, describes latitudinal variations of tracer mixing ratios in terms of their projections onto second-order Legendre polynomials. The present study extends the work of Holton by including tracers with photochemical production in the stratosphere (O3 and NOy). It also includes latitudinal variations in the photochemical sources and sinks, improving slightly the calculated global mean profiles for the long-lived tracers studied by Holton and improving substantially the latitudinal behavior of ozone. Sensitivity tests of the dynamical parameters in the model are performed, showing that the response of the model to changes in vertical residual meridional winds and horizontal diffusion coefficients is similar to that of a full two-dimensional model. A simple ozone perturbation experiment shows the model's ability to reproduce large-scale latitudinal variations in total ozone column depletions as well as ozone changes in the chemically controlled upper stratosphere.
Measurements of energetic solar flare electrons, Jovian electrons, and low-energy solar protons have led to the suggestion that the inner heliosphere is essentially scatter free. Consideration is given to a model in which scattering is only important within the corotating interaction regions (CIR's), while the cavity formed by the CIR's in the inner heliosphere is scatter free, as compared to an interplanetary diffusion model wherein scattering is determined by the solar wind and magnetic field microstructure everywhere in the heliosphere. The two models are compared in terms of the solar wind stream associated Forbush decreases at 1 AU and the longitudinal cosmic ray nucleonic intensity variations at larger heliocentric distances (Pioneer 11 measurements at about 3 AU). It is shown that the diffusion model is able to explain consistently all longitudinal galactic cosmic ray intensity modulation measurements.
The cometary ion pickup process along the sun-comet line at Comet Halley is investigated using a quasi-linear diffusion model including both pitch angle and energy diffusion, adiabatic compression, and convective motion with the solar wind flow. The model results are compared with energetic ion distributions observed by instruments on board the Giotto spacecraft. The observed power spectrum index of magnetic turbulence (gamma) is 2-2.5. The present simulation shows that when gamma was 2, the calculated proton distributions were much more isotropic than the observed ones. The numerical solutions of the quasi-linear diffusion equations show that the isotropization of the pickup ion distribution, particularly at the pickup velocity, is not complete even close to the bow shock. Given the observed turbulence level, quasi-linear theory yields pickup ion energy distributions that agree with the observed ones quite well and easily produces energetic ions with energies up to hundreds of keV.
A 2D model which uses residual circulation and diffusion and a 3D model which uses winds from a stratospheric data assimilation system are used to estimate transport and dispersion of supersonic aircraft exhaust in the lower stratosphere. The seasonal behavior of the exhaust fields in the two models are is similar, but there is a significant difference in the placement of stratosphere/troposphere exchange in the two models. In the 2D model, exhaust transport to the troposphere occurs mostly at high latitudes, while in the 3D model it occurs at middle latitudes and is clearly associated with synoptic scale events. This may be particularly important to assessment calculations, as the pollutant source is mostly in middle latitudes. The 3D model is also used to examine the transport and dispersion of exhaust in three typical flight corridors: North Atlantic, North Pacific, and tropical. There are no systematic differences that suggest that one corridor is inherently more or less polluting than another.