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At least 73 records · Page 4

A Comparison of Major and Minor Species in Io's Exosphere

The atmosphere of the volcanically active moon Io is continuously stripped away through interactions with Jupiter's magnetic field and replenished by volcanically supplied gas. Io's exosphere, the low density region consisting of bound and escaping, non-interacting neutrals, is dominated by oxygen and sulfur atoms formed from the dissociation of SO2. The radial distributions of oxygen and sulfur emissions exhibit an asymmetry between the intensity over Io's leading and trailing hemispheres (Wolven et al. 2001). Sodium, a minor but well studied exospheric component, shows a different asymmetry: the sub-Jupiter exosphere is denser than the anti-Jupiter exosphere (Burger et al. 2001). In addition, the sodium density decreases much faster with distance than the intensities of the oxygen and sulfur emissions. We explore possible sources for these. One possibility is the dependence of the observed emissions lines on plasma flowing through the exosphere. Variations in the electrons affect the excitation rates of the transitions, while leaving the resonantly scattered sodium emission unaffected. The observations may also point to differences in the loss mechanisms from Io's atmosphere: sodium is believed to be sputtered from the atmosphere and surface by high energy ions in the magnetosphere (reviewed Johnson et al 2004; Thomas et al. 2004). It is unclear whether oxygen and sulfur are lost in the same manner, or instead by the dissociation of SO2 near or above the exobase, which would produce a significantly different energy distribution than sputtering, producing the observed differences.

Burger, M. H.↗

Understanding Mercury's Exosphere: Models Derived from MESSENGER Observations: Chapter - 15

The observations of Mercury's exosphere described in Chapter 14 have led to many modeling efforts. Early models were based upon a few simple assumptions and primarily explored the dynamics of sodium atoms pushed anti-sunward by radiation pressure [Ip, 1986; Smyth and Marconi, 1995]. More recently, these early models have been superseded by simulations with an increasing number of interdependent source processes [Leblanc and Johnson, 2003; Mura et al., 2009; Leblanc and Johnson, 2010; Burger et al., 2010, 2012, 2014]. We briefly summarize the source and loss processes before describing the published exosphere models, first for the three species observed almost continuously during the MESSENGER mission by the Ultraviolet and Visible Spectrometer (UVVS) channel of the Mercury Atmospheric and Surface Composition2Spectrometer (MASCS), (Na, Mg and Ca), and then more briefly for other species that have been observed or for which new upper limits have been derived.15.1 Overview of Source and Loss Processes15.1.1 Source Processes15.1.1.1 Thermal DesorptionThermal desorption (or thermal evaporation) is the release of adsorbed atoms from a surface via heating. Thermal desorption is related to the binding energy of the atom on the surface and the vibrational frequency of the bound atom, such that the rate of thermal desorption is given by, (15.1)where TD,

Thermal↗

Sonic Boom Propagation Model Based on a Single-Ray Jacobian

A sonic boom is a nonlinear event whose propagation can be modeled involving two stages. The first stage consists of ray path calculations using linear approximations, while the second stage deals with a nonlinear transport of the acoustic energy along these paths. This presentation discusses a second-order finite difference numerical approach used to predict the ray paths in range-dependent atmospheres and compares it to existing finite difference schemes. The approach is validated using exact solutions obtained for stratified atmospheres. In the second stage, the geometrical spreading effect needed in determining sonic boom waveforms from a Burgers' equation is obtained using a method that only needs a single ray rather than four rays required by most existing sonic boom propagation codes. The single-ray method calculates the Jacobian, associated with the coordinate transformation from a suitable ray coordinate system to the Cartesian coordinate system, directly from the ray tracing equations. While the four-ray method approximates the geometrical spreading using a finite difference scheme involving the four rays, the single-ray method does not rely on this approximation and instead depends purely on the acoustical kinematic properties of the atmosphere. Comparisons of results using these two methods are discussed.

sonic boom↗

Simulation and Regression Modeling of Nasa'S X-59 Low-Boom Carpets Across America

NASA’s X-59 aircraft is predicted to produce a significantly quieter cruise sonic boom than traditional N-wave-producing aircraft. A propagation simulation study was undertaken to quantify loudness levels, exposure size, and variability of the X-59’s low-boom carpet using realistic atmospheric profiles across the contiguous United States of America (CONUS). Near-field pressure data of the X-59 in supersonic cruise from NASA’s fully unstructured Navier–Stokes three-dimensional (known as FUN3D) computational fluid dynamics code were propagated using NASA’s PCBoom code, which solves an enhanced Burgers equation along acoustic rays. Atmospheric profiles from the National Oceanic and Atmospheric Administration’s Climate Forecast System Version 2 database were used for propagation at 138 locations across the CONUS. Carpets at each location were generated for aircraft headings in the four cardinal directions. Over one million X-59 carpets were generated in total. The effects of the heading, season, geography, and climate zone on boom levels and exposure size are presented. Multiple linear regression models were developed to estimate carpet width and loudness metrics across the CONUS. These results inform regulators and mission planners on expected variations in boom levels and carpet extent from atmospheric variations. Understanding potential carpet variability is important when planning community noise surveys using the X-59.

X-59↗

Simulation and Regression Modeling of X-59 Low-Boom Carpets Across America

The NASA X-59 aircraft is predicted to produce a significantly quieter cruise sonic boom than traditional N-wave-producing aircraft. A propagation simulation study was undertaken to quantify loudness levels, exposure size, and variability of the X-59 low-boom carpet using realistic atmospheric profiles across the contiguous United States of America (CONUS). Near-field pressure data of the X-59 in supersonic cruise from NASA’s fully unstructured Navier–Stokes three-dimensional (known as FUN3D) computational fluid dynamics code were propagated using NASA’s PCBoom code, which solves an enhanced Burgers equation along acoustic rays. Atmospheric profiles from the National Oceanic and Atmospheric Administration’s Climate Forecast System Version 2 database were used for propagation at 138 locations across the CONUS. Carpets at each location were generated for aircraft headings in the four cardinal directions. Over one million X-59 carpets were generated in total. The effects of the heading, season, geography, and climate zone on boom levels and exposure size are presented. Multiple linear regression models were developed to estimate carpet width and loudness metrics across the CONUS. These results inform regulators and mission planners on expected variations in boom levels and carpet extent from atmospheric variations. Understanding potential carpet variability is important when planning community noise surveys using the X-59.

X-59↗

Concave-convex growth spirals.

The simple model for introduction of a screw dislocation into a crystal leaves a step in those surfaces of the crystal that intersect the axis of the screw dislocation such that the Burgers vector has a finite component perpendicular to the surfaces. When two parallel surfaces of a crystal intersect the same screw dislocation, the resultant step, on opposite sides of the crystal, face in opposite directions. Consequently, when two such surfaces grow by accretion of the molecules at the steps, the steps wind themselves into spirals that appear to have opposite senses of rotation when viewed along the axis of the screw dislocation. Furthermore, the growth structure that results is a plano convex cone or pyramid centered on the screw dislocation. When growth occurs simultaneously on both sides of a crystal, a doubly convex structure will develop under the control of a singe screw dislocation.

Crystal growth↗

Propagation of weak shock waves through turbulence.

The effect of turbulence on the structure of weak shock waves is investigated. The equilibrium structure is shown to be governed by a balance between nonlinear steepening and the turbulent scattering of acoustic energy out of the main wave direction. The scattered energy appears as perturbations behind the shock front. For conditions typical of sonic booms in atmospheric turbulence the wave structure is governed by a Burgers equation similar to that describing viscous shocks, except that parameters related to the turbulence appear instead of the viscosity coefficient. The magnitude of the perturbations following a shock is estimated from first-order scattering applied to a thickened shock. Predictions of shock thicknesses and perturbations compare favourably with available experimental data.

Plotkin, K. J.↗

Partial implicitization

The steady-state solution to the full Navier-Stokes equations for complicated flows is generally difficult to obtain. The Burgers (1948) equation is used as a model of the Navier-Stokes equations. The steady-state solution is obtained by a one-step explicit technique resulting from a partial implicitization of the difference equation. Stability analysis shows that the technique is unconditionally stable, and numerical tests show the technique to be accurate.

Graves, R. A., Jr.↗

A comparison of numerical solutions to the inviscid equations of fluid motion

The second-order MacCormack method and the third-order Rusanov and Kutler-Warming-Lomax methods are applied to the inviscid 1-d Burgers' equation, wedge flow, and the problem of shock reflection from a rigid boundary. The numerical solution in each case is compared to the exact solution and the quantitative estimates of accuracy are obtained. Results of this study show that the third-order Kutler-Warming-Lomax or the Rusanov methods tuned for minimum dissipation or minimum dispersion provide the most accurate solution in each of the examples considered.

Anderson, D. A.↗

High-order numerical solutions using cubic splines

The cubic spline collocation procedure for the numerical solution of partial differential equations was reformulated so that the accuracy of the second-derivative approximation is improved and parallels that previously obtained for lower derivative terms. The final result is a numerical procedure having overall third-order accuracy for a nonuniform mesh and overall fourth-order accuracy for a uniform mesh. Application of the technique was made to the Burger's equation, to the flow around a linear corner, to the potential flow over a circular cylinder, and to boundary layer problems. The results confirmed the higher-order accuracy of the spline method and suggest that accurate solutions for more practical flow problems can be obtained with relatively coarse nonuniform meshes.

Rubin, S. G.↗

A cubic spline approximation for problems in fluid mechanics

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.↗

The influence of the computational mesh on accuracy for initial value problems with discontinuous or nonunique solutions

Discontinuous, or weak, solutions of the wave equation, the inviscid form of Burgers equation, and the time-dependent, two-dimensional Euler equations are studied. A numerical method of second-order accuracy in two forms, differential and integral, is used to calculate the weak solutions of these equations for several initial value problems, including supersonic flow past a wedge, a double symmetric wedge, and a sphere. The effect of the computational mesh on the accuracy of computed weak solutions including shock waves and expansion phenomena is studied. Modifications to the finite-difference method are presented which aid in obtaining desired solutions for initial value problems in which the solutions are nonunique.

Maccormack, R. W.↗

Viscous flow solutions with a cubic spline approximation

A cubic spline approximation is used for the solution of several problems in fluid mechanics. This procedure provides a high degree of accuracy even with a nonuniform mesh, and leads to a more accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several typical integration schemes are presented. For two-dimensional flows a spline-alternating-direction-implicit (SADI) method is evaluated. The spline procedure is assessed and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.↗

Analytic numerical solutions for shock waves

Study of weak solutions of simple wave equation, inviscid Burgers equation, and Euler equations has resulted in technique for accurate prediction of shock waves occurring in inviscid supersonic flows.

Maccormack, R. W.↗

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗