Numerical experiments on the nonlinear Krook model of the Boltzmann equation
Steady and unsteady state problems and shock wave structure using Krook model of Boltzmann equation
KROOK EQUATION↗
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Results for “Nonlinear waves”
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Langmuir turbulence in the auroral ionosphere 2: Nonlinear theory and simulations
A theoretical interpretation of sounding rocket measurements of intense Langmuir wave fields (less than or equal to 500 mV/m) driven by a stream of 20 eV to 4 keV electrons in the lower auroral zone is developed. This interpretation is based on the ability of the 10 microseconds sampling rate of the wave detector to temporally resolve the structure of the Langmuir wave field envelope. A modified form of the Zakharov equations is used to numerically study beam-driven Langmuir turbulence in the presence of a moderate magnetic field (OMEGA (sub e) approximately equals Omega (sub pe). Strong Landau damping on observed nonthermal scattered electrons, which is treated in a companion paper (Newman et al., this issue), plays an important role by inhibiting backscatter cascade and the development of strong turbulence. A parameterized model of the linear electron stream-driven wave instability is introduced, which incorporates limited quasilinear plateau formation. A reasonable set of parameters is found that yields semiquantitative agreement between observed properties of the Langmuir fields and the results of Zakharov equation simulations, including the amplitude and characteristic frequency of the electric field envelope modulations.
Newman, D. L.↗
Nonlinear Dynamic Behavior of Impact Damage in a Composite Skin-Stiffener Structure
One of the key issues in composite structures for aircraft applications is the early identification of damage. Often, service induced damage does not involve visible plastic deformation, but internal matrix related damage, like delaminations. A wide range of technologies, comprising global vibration and local wave propagation methods can be employed for health monitoring purposes. Traditional low frequency modal analysis based methods are linear methods. The effectiveness of these methods is often limited since they rely on a stationary and linear approximation of the system. The nonlinear interaction between a low frequency wave field and a local impact induced skin-stiffener failure is experimentally demonstrated in this paper. The different mechanisms that are responsible for the nonlinearities (opening, closing and contact) of the distorted harmonic waveforms are separated with the help of phase portraits. A basic analytical model is employed to support the observations.
Ooijevaar, T. H.↗
Use of satellite data and modeling to assess the influence of stratospheric processes on the troposphere
Current research focused on the examination of the effects of ozone heating and Newtonian cooling on the linear stability of transient planetary waves. A finite difference numerical model was developed in which the basic state wind, temperature, and ozone distributions were constructed using ground-based and satellite data. Preliminary results indicate that ozone dynamics interaction may play a more important role in the stability and maintenance of planetary waves than previously thought, particularly in summer when the mean solar zenith angle is smallest and thus ozone heating largest. Examination of the finite amplitude interactions among radiation, ozone, and dynamics was carried out. Self-consistent, coupled equations governing the weakly nonlinear interactions are currently being analyzed to provide a better understanding of wave-mean flow interactions and ozone transport in a continuously stratified model of the troposphere-stratosphere coupled system.
Nathan, Terrence↗
Enhanced damping of Alfven waves in the solar corona by a turbulent wave spectrum
The effect of a background spectrum of Alfven waves on the rate of dissipation of a test shear Alfven wave is numerically calculated. The results demonstrate that as the classical resistivity eta and classical viscosity mu become small, the damping rate of the Alfven wave remains large and depends only on the amplitude for the scalar potential of the wave spectrum and the wavenumber of the Alfven wave. The damping rate is virtually independent of eta and mu. The wave spectrum need not be turbulent or stochastic to affect the damping rate. The dissipation rate is nonlinear enhanced by nonstochastic spectra as well as by stochastic spectra if two conditions are met. First, the perpendicular magnetic field associated with Alfven wave spectrum must exceed a certain collision-frequency threshold and second, for nonstochastic spectra only, the magnetic field must exceed a threshold proportional to the parallel wavenumber of the shear Alfven wave. These conditions can be easily satisfied in the solar corona.
Kleva, Robert G.↗
Nonlinear stability of solar type III radio bursts. I - Theory
A theory of the excitation of solar type III bursts is presented. Electrons initially unstable to the linear bump-in-tail instability are shown to rapidly amplify Langmuir waves to energy densities characteristic of strong turbulence. The three-dimensional equations which describe the strong coupling (wave-wave) interactions are derived. For parameters characteristic of the interplanetary medium the equations reduce to one-dimension. In that case the oscillating two-stream instability (OTSI) is the dominant nonlinear instability. OTSI is stabilized through the production of nonlinear ion density fluctuations that efficiently scatter Langmuir waves out of resonance with the electron beam. An analytical model of the electron distribution function is also developed which is used to estimate the total energy losses suffered by the electron beam as it propagates from the solar corona to 1 AU and beyond.
Smith, R. A.↗
Nonlinear interaction between whistlers.
Whistlers nonlinear interaction during cold magnetoplasma propagation, considering energy exchanges between waves
Crawford, F. W.↗
Higher order approximations in the theory of longitudinal plasma oscillations. II
Small amplitude nonlinear longitudinal plasma oscillations perturbation analysis, discussing Landau damping, monochromatic wave evolution and independent variable expansion
Axford, W. I.↗
ISEE particle observations of surface waves at the magnetopause boundary layer
The dual-spacecraft ISEE mission provides a unique opportunity to study the motions of the magnetopause and adjacent boundary layer. By comparing high-time-resolution energetic particle data from ISEE 1 to those of ISEE 2, the velocity and orientation of the inner boundary of the boundary layer can be determined. Two cases are presented. In one, tailward propagating sinusoidally shaped surface waves with a wavelength in excess of 42,000 km and an amplitude of approximately 5000 km are found. In the other, surface waves are indicated with a wavelength of approximately 40,000 km and an amplitude of approximately 11,000 km having steepened nonsinusoidal shapes. The existence of such large-amplitude waves suggests that the particle dynamics near the magnetopause support nonlinear processes.
Couzens, D.↗
Comet-solar wind interaction through ion-proton beam instability
The acceleration of cometary ions in the distant cometary tail by an electromagnetic beam instability, which is caused by the relative drift velocity between the cometary ions and solar protons is studied. The linear phase of the instability is analyzed by numerical evaluation of the Vlasov dispersion relation. A particle simulation is used to study the nonlinear phase of the instability. Right-hand polarized cyclotron waves are made unstable by the presence of ion beams. The cometary tail ions are accelerated mainly during the reduced-growth phase of the instability. The cyclotron waves cause momentum transfer from solar wind protons to cometary tail ions. The acceleration of cometary ions through the electromagnetic beam instability is found to be 500-5000 cm/s-squared.
Price, Channon P.↗
TS - Dean interactions in curved channel flow
A weakly nonlinear theory is developed to study the interaction of TS waves and Dean vortices in curved channel flow. The prediction obtained from the theory agree well with results obtained from direct numerical simulations of curved channel flow, especially for low amplitude disturbances. At low Reynolds numbers the wave interaction is generally stabilizing to both disturbances, though as the Reynolds number increases, many linearly unstable TS waves are further destabilized by the presence of Dean vortices.
Singer, Bart A.↗
Theoretical models of gas dynamics and star formation in interacting ring galaxies
A series of one and two dimensional hydrodynamic simulations of a ring wave in interstellar gas disks was completed. These calculations included nonlinear source terms to model the effects of interstellar interactions and star formation, as well as the spatial-temporal gas flow. Toomre's kinematical model was merged with the Arnold, Shandarin, and Zeldovich 'pancake' theory of caustics in galaxy formation. The resulting theory can describe almost all the structure in restricted three-body simulations of single-pass collisions, even with multi-component potentials. Off-center galactic collisions were studied to understand the dynamics involved. Multi-color optical and near-infrared observations of faint tidal features were performed in about two dozen interacting galaxies selected from the Arp atlas. This sample provided evidence for ongoing star formation in tidal structures, and even enhancements of star formation in some cases. The task of assembling the data for gas-rich, late-type galaxies, was undertaken to see if a more coherent picture of the gas distribution would emerge from the more complete data. Analytic solutions of the equations with subsonic flows to balance gas consumption for expulsion form a galactic fountain were also derived.
Struck-Marcell, Curtis↗
Anisotropy and minimum variance directions of solar wind fluctuations in the outer heliosphere
Voyager 2 magnetic field and plasma data are examined over time intervals of 1 to 12 hours in the heliospheric range of 1 to 10 AU to study the evolution of the anisotropy of solar wind fluctuations. Consistent with previous results, the directions of minimum variance vectors of magnetic fluctuations are found to be close to the mean magnetic field direction with an increasing component along the field at larger scales. At large radial distances there is more spread in the minimum variance directions than at smaller radial distances. The power in smaller-scale fluctuations in the magnetic field components perpendicular to the local mean field B(0) is in the ratio of about 5:1 near 1 AU at the scale of 1 hour but decreases to about 3:1 further out. No evidence for selective enhancement of out-of-the-ecliptic components of fluctuations is found. In contrast to results for field fluctuations, analysis of velocity fluctuations shows that the minimum variance direction systematically remains more radially oriented and becomes increasingly less oriented along B(0) with increasing heliocentric distance. The velocity fluctuations are generally more isotropic than the magnetic fluctuations. The observations cannot be explained by a superposed wave picture, and thus are consistent with the view that nonlinear turbulent evolution is responsible for the anisotropy in the fluctuations.
Klein, Larry W.↗
Optimal Signal Filtration in Optical Sensors with Natural Squeezing of Vacuum Noises
The structure of optimal receiver is discussed for optical sensor measuring a small displacement of probe mass. Due to nonlinear interaction of the field and the mirror, a reflected wave is in squeezed state (natural squeezing), two quadratures of which are correlated and therefore one can increase signal-to-noise ratio and overcome the SQL. A measurement procedure realizing such correlation processing of two quadratures is clarified. The required combination of quadratures can be produced via mixing of pump field reflected from the mirror with local oscillator phase modulated field in duel-detector homodyne scheme. Such measurement procedure could be useful not only for resonant bar gravitational detector but for laser longbase interferometric detectors as well.
Gusev, A. V.↗
Frequency conversion system
Laser diode pumped mid-IR wavelength sources include at least one high power, near-IR wavelength, injection and/or sources wherein one or both of such sources may be tunable providing a pump wave output beam to a quasi-phase matched (QPM) nonlinear frequency mixing (NFM) device. The NFM device may be a difference frequency mixing (DFM) device or an optical parametric oscillation (OPO) device. Wavelength tuning of at least one of the sources advantageously provides the ability for optimizing pump or injection wavelengths to match the QPM properties of the NFM device enabling a broad range of mid-IR wavelength selectivity. Also, pump powers are gain enhanced by the addition of a rare earth amplifier or oscillator, or a Raman/Brillouin amplifier or oscillator between the high power source and the NFM device. Further, polarization conversion using Raman or Brillouin wavelength shifting is provided to optimize frequency conversion efficiency in the NFM device.
Sanders, Steven↗
Development of Multi-Physics Dynamics Models for High-Frequency Large-Amplitude Structural Response Simulation
An analytic approach is demonstrated to reveal potential pyroshock-driven dynamic effects causing power losses in the Thermo-Electric (TE) module bars of the Mars Science Laboratory (MSL) Multi-Mission Radioisotope Thermoelectric Generator (MMRTG). This study utilizes high-fidelity finite element analysis with SIERRA/PRESTO codes to estimate wave propagation effects due to large-amplitude suddenly-applied pyro shock loads in the MMRTG. A high fidelity model of the TE module bar was created with approximately 30 million degrees-of-freedom (DOF). First, a quasi-static preload was applied on top of the TE module bar, then transient tri-axial acceleration inputs were simultaneously applied on the preloaded module. The applied input acceleration signals were measured during MMRTG shock qualification tests performed at the Jet Propulsion Laboratory. An explicit finite element solver in the SIERRA/PRESTO computational environment, along with a 3000 processor parallel super -computing framework at NASA AMES, was used for the simulation. The simulation results were investigated both qualitatively and quantitatively. The predicted shock wave propagation results provide detailed structural responses throughout the TE module bar, and key insights into the dynamic response (i.e., loads, displacements, accelerations) of critical internal spring/piston compression systems, TE materials, and internal component interfaces in the MMRTG TE module bar. They also provide confidence on the viability of this high-fidelity modeling scheme to accurately predict shock wave propagation patterns within complex structures. This analytic approach is envisioned for modeling shock sensitive hardware susceptible to intense shock environments positioned near shock separation devices in modern space vehicles and systems.
Shock Waves↗
Interactions between gravity waves and cold air outflows in a stably stratified uniform flow
Interactions between gravity waves and cold air outflows in a stably stratified uniform flow forced by various combinations of prescribed heat sinks and sources are studied using a hydrostatic two-dimensional nonlinear numerical model. The formation time for the development of a stagnation point or reversed flow at the surface is not always directly proportional to the Froude number when wave reflections exist from upper levels. A density current is able to form by the wave-otuflow interaction, even though the Froude number is greater than a critical value. This is the result of the wave-outflow interaction shifting the flow response to a different location in the characteristic parameter space. A density current is able to form or be destroyed due to the wave-outflow interaction between a traveling gravity wave and cold air outflow. This is proved by performing experiments with a steady-state heat sink and an additional transient heat source. In a quiescent fluid, a region of cold air, convergence, and upward motion is formed after the collision between two outflows produced by two prescribed heat sinks. After the collision, the individual cold air outflows lose their own identity and merge into a single, stationary, cold air outflow region. Gravity waves tend to suppress this new stationary cold air outflow after the collision. The region of upward motion associated with the collision is confined to a very shallow layer. In a moving airstream, a density current produced by a heat sink may be suppressed or enhanced nonlinearly by an adjacent heat sink due to the wave-outflow interaction.
Lin, Yuh-Lang↗
Nonlinear dynamic response of a uni-directional model for the tile/pad space shuttle thermal protection system
A unidirectional analysis of the nonlinear dynamic behavior of the space shuttle tile/pad thermal protection system is developed and examined for imposed sinusoidal and random motions of the shuttle skin and/or applied tile pressure. The analysis accounts for the highly nonlinear stiffening hysteresis and viscous behavior of the pad which joins the tile to the shuttle skin. Where available, experimental data are used to confirm the validity of the analysis. Both analytical and experimental studies reveal that the system resonant frequency is very high for low amplitude oscillations but decreases rapidly to a minimum value with increasing amplitude. Analytical studies indicate that with still higher amplitude the resonant frequency increases slowly. The nonlinear pad is also responsible for the analytically and experimentally observed distorted response wave shapes having high sharp peaks when the system is subject to sinusoidal loads. Furthermore, energy dissipation in the pad is studied analytically and it is found that the energy dissipated is sufficiently high to cause rapid decay of dynamic transients. Nevertheless, the sharp peaked nonlinear responses of the system lead to higher magnification factors than would be expected in such a highly damped linear system.
Housner, J. M.↗