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NASA NTRS1997

Nonlinear wave particle interaction in the Earth's foreshock

The possibility that ion beams could provide a free energy source for driving an ion/ion instability responsible for the ULF wave occurrence is investigated. For this, the wave dispersion relation with the observed parameters is solved. Secondly, it is shown that the ring-like distributions could then be produced by a coherent nonlinear wave-particle interaction. It tends to trap the ions into narrow cells in velocity space centered around a well-defined pitch-angle, directly related to the saturation wave amplitude in the analytical theory. The theoretical predictions with the observations are compared.

Mazelle, C.↗

NASA NTRS2000

The Generation of Smooth High Speed Solar Wind From Plume-Interplume Mixing

Ulysses has shown that fast solar wind is extremely smooth, with a variance of less than 5%, in contrast to slow wind with a variance of approximately 30%. Now UVCS has produced the surprising result that the flow speed within coronal holes, the source of fast wind, is not at all smooth. Specifically, Giordano et al. (ApJ, v531, L79-L82, 2000) report that at 1.7 R(sub SUN) the interplume flow speed is typically more than twice the plume flow speed. Other less direct evidence supports this same result, with speeds from less than 300 to over 1000 km/s reported at approximately 5 R(sub SUN). This presents the paradox of how strongly differing plume and interplume flow speeds can exist near the Sun and be absent far from the Sun. The only answer is that plume and interplume material or momentum must be strongly mixed and that the mixing must occur mainly inside 0.3 AU to be consistent with Helios observations of smooth fast wind. Pressure balance structures (PBSs) and He abundance anomalies (Reisenfeld, et al., GRL, v26(13), 1805-1808, 1999) have been identified as interplanetary remnants of plumes, implying momentum mixing is the dominant coronal process. One possible source for plume/interplume momentum mixing is MHD Kelvin-Helmholtz (KH) shear instabilities occurring on the velocity shear interfaces. The velocity shear is a source of free energy and KH fluctuations could, through nonlinear cascade, provide the forcing required for the plasma oscillations (Cranmer, ApJ, v532, 1197-1208, 2000) reported to exist in coronal holes. The physical properties in coronal holes are now sufficiently well known that we can show plume/interplume shear interfaces become unstable to the KH instability at 5 - 10 R(sub SUN). The KH dispersion relation can be used to analyze marginal stability, the most unstable wavelengths, and linear growth rates. Numerical simulations can be used to verify results from the linear analysis and study the nonlinear development of KH modes. Here we will describe the marginal stability criterion for the KH instability, how and where this condition is met in the corona, and the possible character of the resultant fluctuations.

Suess, Steve↗

NASA NTRS2001

Dynamics of Aqueous Foam Drops

We develop a model for the nonlinear oscillations of spherical drops composed of aqueous foam. Beginning with a simple mixture law, and utilizing a mass-conserving bubble-in-cell scheme, we obtain a Rayleigh-Plesset-like equation for the dynamics of bubbles in a foam mixture. The dispersion relation for sound waves in a bubbly liquid is then coupled with a normal modes expansion to derive expressions for the frequencies of eigenmodal oscillations. These eigenmodal (breathing plus higher-order shape modes) frequencies are elicited as a function of the void fraction of the foam. A Mathieu-like equation is obtained for the dynamics of the higher-order shape modes and their parametric coupling to the breathing mode. The proposed model is used to explain recently obtained experimental data.

Akhatov, Iskander↗

NASA NTRS2000

Direct Numerical Simulation of Automobile Cavity Tones

The Navier Stokes equation is solved computationally by the Dispersion-Relation-Preserving (DRP) scheme for the flow and acoustic fields associated with a laminar boundary layer flow over an automobile door cavity. In this work, the flow Reynolds number is restricted to R(sub delta*) < 3400; the range of Reynolds number for which laminar flow may be maintained. This investigation focuses on two aspects of the problem, namely, the effect of boundary layer thickness on the cavity tone frequency and intensity and the effect of the size of the computation domain on the accuracy of the numerical simulation. It is found that the tone frequency decreases with an increase in boundary layer thickness. When the boundary layer is thicker than a certain critical value, depending on the flow speed, no tone is emitted by the cavity. Computationally, solutions of aeroacoustics problems are known to be sensitive to the size of the computation domain. Numerical experiments indicate that the use of a small domain could result in normal mode type acoustic oscillations in the entire computation domain leading to an increase in tone frequency and intensity. When the computation domain is expanded so that the boundaries are at least one wavelength away from the noise source, the computed tone frequency and intensity are found to be computation domain size independent.

Kurbatskii, Konstantin↗

NASA NTRS2001

Electronic Structure and Properties of Deformed Carbon Nanotubes

A theoretical framework based on Huckel tight-binding model has been formulated to analyze the electronic structure of carbon nanotubes under uniform deformation. The model successfully quantifies the dispersion relation, density of states and bandgap change of nanotubes under uniform stretching, compression, torsion and bending. Our analysis shows that the shifting of the Fermi point away from the Brillouin zone vertices is the key reason for these changes. As a result of this shifting, the electronic structure of deformed carbon nanotubes varies dramatically depending on their chirality and deformation mode. Treating the Fermi point as a function of strain and tube chirality, the analytical solution preserves the concise form of undeformed carbon nanotubes. It predicts the shifting, merging and splitting of the Van Hove singularities in the density of states and the zigzag pattern of bandgap change under strains. Four orbital tight-binding simulations of carbon nanotubes under uniform stretching, compression, torsion and bending have been performed to verify the analytical solution. Extension to more complex systems are being performed to relate this analytical solution to the spectroscopic characterization, device performance and proposed quantum structures induced by the deformation. The limitations of this model will also be discussed.

Yang, Liu↗

NASA NTRS1994

Numerical Wave Propagation 211 Based on Wave Primitives

Compact higher order finite difference equations are applied to a sequence of problems in wave propagation and aeroacoustics. Systems of PDE's are reduced to a sequence of simple wave primitives using a local eigenvector decomposition. The wave primitives are first order PDE's in two independent variable and allow natural boundary conditions to be imposed for both single- and multidimensional problems. The method uses a "discrete dispersion relation" approach to obtain high order approximations to the wave primitives on a 3 spatial point / 2 time level computational molecule. The scheme is fourth order accurate for the class of system with constant coefficients, e.g., those that support exponential solutions. Weakly non-linear PDE's are solved in a similar manner using a variant of the "method of frozen coefficients." Experience with the new algorithm for linear, non-linear, and multi-dimensional test problems will be described.

Davis, Sanford S.↗

NASA NTRS2001

Plasma Waves Observed in the Cusp Turbulent Boundary Layer: An Analysis of High Time Resolution Wave and Particle Measurements from the Polar Spacecraft

The boundary layer located in the cusp and adjacent to the magnetopause is a region that is quite turbulent and abundant with waves. The Polar spacecraft's orbit and sophisticated instrumentation are ideal for studying this region of space. Our analysis of the waveform data obtained in this turbulent boundary layer shows broadband magnetic noise extending up to a few kilohertz (but less than the electron cyclotron frequency); sinusoidal bursts (a few tenths of a second) of whistler mode waves at around a few tens of hertz, a few hundreds of hertz, and just below the electron cyclotron frequency; and bipolar pulses, interpreted as electron phase-space holes. In addition, bursts of electron cyclotron harmonic waves are occasionally observed with magnetic components. We show evidence of broadband electrostatic bursts covering a range of approx. 3 to approx. 25 kHz (near but less than the plasma frequency) occurring in packets modulated at the frequency of some of the whistler mode waves. On the basis of high time resolution particle data from the Polar HYDRA instrument, we show that these bursts are consistent with generation by the resistive medium instability. The most likely source of the whistler mode waves is the magnetic reconnection site closest to the spacecraft, since the waves are observed propagating both toward and away from the Earth, are bursty, which is often the case with reconnection, and do not fit on the theoretical cold plasma dispersion relation curve.

Pickett, J. S.↗

NASA NTRS2001

Vorticity Transport and Wave Emission in the Protoplanetary Nebula

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler/Energy equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the nebula to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived using the simulation data and compared with analytical dispersion relations from the linearized Euler/Energy equations.

Davis, S. S.↗

NASA NTRS2002

Vorticity Transport and Wave Emission In A Protoplanetary Disk

Higher order numerical algorithms (4th order in time, 3rd order in space) are applied to the Euler equations and are used to examine vorticity transport and wave motion in a non-self gravitating, initially isentropic Keplerian disk. In this talk we will examine the response of the disk to an isolated vortex with a circulation about equal to the rotation rate of Jupiter. The vortex is located on the 4 AU circle and the nebula is simulated from 1 to 24 AU. We show that the vortex emits pressure-supported density and Rossby-type wave packets before it decays within a few orbits. The acoustic density waves evolve into weak (non entropy preserving) shock waves that propagate over the entire disk. The Rossby waves remain in the vicinity of the initial vortex disturbance, but are rapidly damped. Temporal frequencies and spatial wavenumbers are derived from the nonlinear simulation data and correlated with analytical dispersion relations from the linearized Euler and energy equations.

Davis, S. S.↗

NASA NTRS1999

Fractal fluctuations in cardiac time series

Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.

NASA Discipline Cardiopulmonary↗

NASA NTRS2003

Bose Condensation at He-4 Interfaces

Path Integral Monte Carlo was used to calculate the Bose-Einstein condensate fraction at the surface of a helium film at T = 0:77 K, as a function of density. Moving from the center of the slab to the surface, the condensate fraction was found to initially increase with decreasing density to a maximum value of 0.9, before decreasing. Long wavelength density correlations were observed in the static structure factor at the surface of the slab. A surface dispersion relation was calculated from imaginary-time density-density correlations. Similar calculations of the superfluid density throughout He-4 droplets doped with linear impurities (HCN)(sub n) are presented. After deriving a local estimator for the superfluid density distribution, we find a decreased superfluid response in the first solvation layer. This effective normal fluid exhibits temperature dependence similar to that of a two-dimensional helium system.

Draeger, E. W.↗

NASA NTRS2006

Direct Measurement of Wave Kernels in Time-Distance Helioseismology

Solar f-mode waves are surface-gravity waves which propagate horizontally in a thin layer near the photosphere with a dispersion relation approximately that of deep water waves. At the power maximum near 3 mHz, the wavelength of 5 Mm is large enough for various wave scattering properties to be observable. Gizon and Birch (2002,ApJ,571,966)h ave calculated kernels, in the Born approximation, for the sensitivity of wave travel times to local changes in damping rate and source strength. In this work, using isolated small magnetic features as approximate point-sourc'e scatterers, such a kernel has been measured. The observed kernel contains similar features to a theoretical damping kernel but not for a source kernel. A full understanding of the effect of small magnetic features on the waves will require more detailed modeling.

Duvall, T. L., Jr.↗

NASA NTRS2006

3D Relativistic Magnetohydrodynamic Simulations of Magnetized Spine-Sheath Relativistic Jets

Numerical simulations of weakly magnetized and strongly magnetized relativistic jets embedded in a weakly magnetized and strongly magnetized stationary or weakly relativistic (v = c/2) sheath have been performed. A magnetic field parallel to the flow is used in these simulations performed by the new GRMHD numerical code RAISHIN used in its RMHD configuration. In the numerical simulations the Lorentz factor gamma = 2.5 jet is precessed to break the initial equilibrium configuration. In the simulations sound speeds are less than or equal to c/the square root of 3 in the weakly magnetized simulations and less than or equal to 0.56 c in the strongly magnetized simulations. The Alfven wave speed is less than or equal to 0.07 c in the weakly magnetized simulations and less than or equal to 0.56 c in the strongly magnetized simulations. The results of the numerical simulations are compared to theoretical predictions from a normal mode analysis of the linearized relativistic magnetohydrodynamic (RMHD) equations capable of describing a uniform axially magnetized cylindrical relativistic jet embedded in a uniform axially magnetized relativistically moving sheath. The theoretical dispersion relation allows investigation of effects associated with maximum possible sound speeds, Alfven wave speeds near light speed and relativistic sheath speeds. The prediction of increased stability of the weakly magnetized system resulting from c/2 sheath speeds and the stabilization of the strongly magnetized system resulting from c/2 sheath speeds is verified by the numerical simulation results.

Mizuno, Yosuke↗

NASA NTRS2003

Helicon Wave Physics Impacts on Electrodeless Thruster Design

Effective generation of helicon waves for high density plasma sources is determined by the dispersion relation and plasma power balance. Helicon wave plasma sources inherently require an applied magnetic field of .01-0.1 T, an antenna properly designed to couple to the helicon wave in the plasma, and an rf power source in the 10-100 s of MHz, depending on propellant choice. For a plasma thruster, particularly one with a high specific impulse (>2000 s), the physics of the discharge would also have to address the use of electron cyclotron resonance (ECR) heating and magnetic expansion. In all cases the system design includes an optimized magnetic field coil, plasma source chamber, and antenna. A preliminary analysis of such a system, calling on experimental data where applicable and calculations where required, has been initiated at Glenn Research Center. Analysis results showing the mass scaling of various components as well as thruster performance projections and their impact on thruster size are discussed.

Gilland, James↗

NASA NTRS2007

Helicon Wave Physics Impacts on Electrodeless Thruster Design

Gilland, James H.↗

NASA NTRS2006

Small-Scale Gravity Waves in ER-2 MMS/MTP Wind and Temperature Measurements during CRYSTAL-FACE

Lower stratospheric wind and temperature measurements made from NASA's high-altitude ER-2 research aircraft during the CRYSTAL-FACE campaign in July 2002 were analyzed to retrieve information on small scale gravity waves (GWs) at the aircraft's flight level (typically approximately 20 km altitude). For a given flight segment, the S-transform (a Gaussian wavelet transform) was used to search for and identify small horizontal scale GW events, and to estimate their apparent horizontal wavelengths. The horizontal propagation directions of the events were determined using the Stokes parameter method combined with the cross S-transform analysis. The vertical temperature gradient was used to determine the vertical wavelengths of the events. GW momentum fluxes were calculated from the cross S-transform. Other wave parameters such as intrinsic frequencies were calculated using the GW dispersion relation. More than 100GW events were identified. They were generally high frequency waves with vertical wavelength of approximately 5 km and horizontal wavelength generally shorter than 20 km. Their intrinsic propagation directions were predominantly toward the east, whereas their ground-based propagation directions were primarily toward the west. Among the events, approximately 20% of them had very short horizontal wavelength, very high intrinsic frequency, and relatively small momentum fluxes, and thus they were likely trapped in the lower stratosphere. Using the estimated GW parameters and the background winds and stabilities from the NCAR/NCEP reanalysis data, we were able to trace the sources of the events using a simple reverse ray-tracing. More than 70% of the events were traced back to convective sources in the troposphere, and the sources were generally located upstream of the locations of the events observed at the aircraft level. Finally, a probability density function of the reversible cooling rate due to GWs was obtained in this study, which may be useful for cirrus cloud models.

Wang, L.↗

NASA NTRS2011

A High-Resolution Capability for Large-Eddy Simulation of Jet Flows

A large-eddy simulation (LES) code that utilizes high-resolution numerical schemes is described and applied to a compressible jet flow. The code is written in a general manner such that the accuracy/resolution of the simulation can be selected by the user. Time discretization is performed using a family of low-dispersion Runge-Kutta schemes, selectable from first- to fourth-order. Spatial discretization is performed using central differencing schemes. Both standard schemes, second- to twelfth-order (3 to 13 point stencils) and Dispersion Relation Preserving schemes from 7 to 13 point stencils are available. The code is written in Fortran 90 and uses hybrid MPI/OpenMP parallelization. The code is applied to the simulation of a Mach 0.9 jet flow. Four-stage third-order Runge-Kutta time stepping and the 13 point DRP spatial discretization scheme of Bogey and Bailly are used. The high resolution numerics used allows for the use of relatively sparse grids. Three levels of grid resolution are examined, 3.5, 6.5, and 9.2 million points. Mean flow, first-order turbulent statistics and turbulent spectra are reported. Good agreement with experimental data for mean flow and first-order turbulent statistics is shown.

DeBonis, James R.↗

NASA NTRS2013

Solutions of the Taylor-Green Vortex Problem Using High-Resolution Explicit Finite Difference Methods

A computational fluid dynamics code that solves the compressible Navier-Stokes equations was applied to the Taylor-Green vortex problem to examine the code s ability to accurately simulate the vortex decay and subsequent turbulence. The code, WRLES (Wave Resolving Large-Eddy Simulation), uses explicit central-differencing to compute the spatial derivatives and explicit Low Dispersion Runge-Kutta methods for the temporal discretization. The flow was first studied and characterized using Bogey & Bailley s 13-point dispersion relation preserving (DRP) scheme. The kinetic energy dissipation rate, computed both directly and from the enstrophy field, vorticity contours, and the energy spectra are examined. Results are in excellent agreement with a reference solution obtained using a spectral method and provide insight into computations of turbulent flows. In addition the following studies were performed: a comparison of 4th-, 8th-, 12th- and DRP spatial differencing schemes, the effect of the solution filtering on the results, the effect of large-eddy simulation sub-grid scale models, and the effect of high-order discretization of the viscous terms.

DeBonis, James R.↗