Propagation of light pulses in a laser amplifier
Light pulses propagation in nonlinear laser medium, obtaining equations of motion for density matrix
Icsevgi, A.↗
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Propagation of sonic booms and other weak nonlinear waves through turbulence
Sonic boom and explosion shock wave propagation over long distances through turbulence modeled by sound speed fluctuation, including acoustic scattering effect
George, A. R.↗
Lagrangian description of warm plasmas
Efforts are described to extend the averaged Lagrangian method of describing small signal wave propagation and nonlinear wave interaction, developed by earlier workers for cold plasmas, to the more general conditions of warm collisionless plasmas, and to demonstrate particularly the effectiveness of the method in analyzing wave-wave interactions. The theory is developed for both the microscopic description and the hydrodynamic approximation to plasma behavior. First, a microscopic Lagrangian is formulated rigorously, and expanded in terms of perturbations about equilibrium. Two methods are then described for deriving a hydrodynamic Lagrangian. In the first of these, the Lagrangian is obtained by velocity integration of the exact microscopic Lagrangian. In the second, the expanded hydrodynamic Lagrangian is obtained directly from the expanded microscopic Lagrangian. As applications of the microscopic Lagrangian, the small-signal dispersion relations and the coupled mode equations are derived for all possible waves in a warm infinite, weakly inhomogeneous magnetoplasma, and their interactions are examined.
Kim, H.↗
Report of the Plasma Physics and Environmental Perturbation Laboratory (PPEPL) working groups. Volume 2: Wave experiments working group
The area of wave experiments for the PPEPL is considered in broad terms. It was found that most experiments in this area can be classified typically by a few generalized experiments. These experiment possibilities are discussed in terms of advantages, disadvantages, and probable areas for future investigation. It was concluded that the areas where wave experiments have the most promise are wave sources, wave propagation, and nonlinear interactions and should be implemented in that order. It was recommended that the PPEPL facility remain sufficiently flexible to handle new ideas as they appear, and a continuing effort should be made to solicit new ideas and approaches. It was also felt that detailed investigations should begin as soon as possible in the areas of antennas, both conventional and particle types, and wave-particle interaction experiments. For Vol. 1, see N74-28169; for Vol. 3, see N74-28171.
Source record↗
Atmospheric absorption of high frequency noise and application to fractional-octave bands
Pure tone sound absorption coefficients were measured at 1/12 octave intervals from 4 to 100 KHz at 5.5K temperature intervals between 255.4 and 310.9 K and at 10 percent relative humidity increments between 0 percent and saturation in a large cylindrical tube (i.d., 25.4 cm; length, 4.8 m). Special solid-dielectric capacitance transducers, one to generate bursts of sound waves and one to terminate the sound path and detect the tone bursts, were constructed to fit inside the tube. The absorption was measured by varying the transmitter receiver separation from 1 to 4 m and observing the decay of multiple reflections or change in amplitude of the first received burst. The resulting absorption was compared with that from a proposed procedure for computing sound absorption in still air. Absorption of bands of noise was numerically computed by using the pure tone results. The results depended on spectrum shape, on filter type, and nonlinearly on propagation distance. For some of the cases considered, comparison with the extrapolation of ARP-866A showed a difference as large as a factor of 2. However, for many cases, the absorption for a finite band was nearly equal to the pure tone absorption at the center frequency of the band. A recommended prediction procedure is described for 1/3 octave band absorption coefficients.
Shields, F. D.↗
Effects of accumulated film layers on the accuracy of quartz film thickness monitors
The effect of accumulation layers on the accuracy of quartz thin-film thickness monitors is evaluated. Use of an expanded plane wave ultrasonic propagation theory correctly accounts for observed experimental data. The magnitude of the maximum errors calculated for simply reversing the order of a series of aluminum gold deposits is on the order of 5%. If one totally neglects intervening layers, multiple film propagation and nonlinearity can produce errors greater than 50%.
Heyman, J. S.↗
Experimental study of the dynamics of a ruby laser pumped by a CW argon-ion laser
A study of the dynamics of a ruby laser pumped by a CW argon-ion laser is presented. The ruby laser is predominantly stable but has two accessible unstable states. One state exhibits chaotic output, while the other results in regular self-pulsing. The conditions needed for instability are discussed and homodyne spectra and temporal maps of the phase-space attractors are obtained. In addition, a numerical simulation of nonlinear beam propagation in ruby is presented that shows that strong deviations from plane-wave behavior exist, and that transverse effects must be incorporated into theoretical models of the instability.
Afzal, R. S.↗
The sonic boom of an oblique flying wing
An analysis of sonic boom characteristics of an oblique flying wing is presented. The wing, represented by a slewed lift and area-distribution as well as a panel geometry, promises a reduction of sonic boom signature. For every azimuth angle these distributions are represented by an equivalent body. The near-field pressure signature is determined by using the Whitham F-function with a correction to account for nonlinear wave propagation. The geometric asymmetry leads to an asymmetrical sonic boom beneath the flight track with bow shocks between 1.0 and 1.5 PSF. Due to favorable volume-lift interference the aft shock has only half the amplitude of the bow shock. A fast numerical method is described to calculate the perceived loudness.
Kroo, Ilan↗
Transport of energy by disturbances in arbitrary steady flows
An exact equation governing the transport of energy associated with disturbances in an arbitrary steady flow is derived. The result is a generalization of the familiar concept of acoustic energy and is suggested by a perturbation expansion of the general energy equation of fluid mechanics. A disturbance energy density and flux are defined and identified as exact fluid dynamic quantities whose leading-order regular perturbation representations reduce in various special cases to previously known results. The exact equation on disturbance energy is applied to a simple example of nonlinear wave propagation as an illustration of its general utility in situations where a linear description of the disturbance is inadequate.
Myers, M. K.↗
On acoustic radiation from a vibrating panel
An experimental and numerical study of the response and radiation from an acoustically loaded aircraft panel is presented. In the experiment, the panel is excited by a normally incident, harmonic wave. Measurements of the panel response and the resulting transmitted pressure are made in both the near- and acoustic far-fields. The numerical computations model the experiment and in particular account for the full coupling between the panel and the surrounding three dimensional acoustic fluid. The results demonstrate that for a sufficiently high excitation level, the panel response becomes nonlinear. The nonlinearity is characterized by the appearance of harmonics and subharmonics in the power spectral densities of the panel motion and consequently in the resulting acoustic radiation. The primary characteristic of the far-field acoustic radiation is the increase in harmonic content relative to the fundamental and subharmonics with increasing distance from the panel. This is shown to be a result of linear and weakly nonlinear wave propagation effects. The numerical results show that the radiated far-field pressure is strongly dependent on the position of the measurement point with respect to the panel center. The experimental and numerical results are in good qualitative agreement.
Frendi, Abdelkader↗
Boundary Conditions for Unsteady Compressible Flows
This paper explores solutions to the spherically symmetric Euler equations. Motivated by the work of Hagstrom and Hariharan and Geer and Pope, we modeled the effect of a pulsating sphere in a compressible medium. The literature available on this suggests that an accurate numerical solution requires artificial boundary conditions which simulate the propagation of nonlinear waves in open domains. Until recently, the boundary conditions available were in general linear and based on nonreflection. Exceptions to this are the nonlinear nonreflective conditions of Thompson, and the nonlinear reflective conditions of Hagstrom and Hariharan. The former are based on the rate of change of the incoming characteristics; the latter rely on asymptotic analysis and the method of characteristics and account for the coupling of incoming and outgoing characteristics. Furthermore, Hagstrom and Hariharan have shown that, in a test situation in which the flow would reach a steady state over a long time, Thompson's method could lead to an incorrect steady state. The current study considers periodic flows and includes all possible types and techniques of boundary conditions. The technique recommended by Hagstrom and Hariharan proved superior to all others considered and matched the results of asymptotic methods that are valid for low subsonic Mach numbers.
Hariharan, S. I.↗
Benchmark problems in computational aeroacoustics
A recent directive at NASA Langley is aimed at numerically predicting principal noise sources. During my summer stay, I worked with high-order ENO code, developed by Dr. Harold Atkins, for solving the unsteady compressible Navier-Stokes equations, as it applies to computational aeroacoustics (CAA). A CAA workshop, composed of six categories of benchmark problems, has been organized to test various numerical properties of code. My task was to determine the robustness of Atkins' code for these test problems. In one category, we tested the nonlinear wave propagation of the code for the one-dimensional Euler equations, with initial pressure, density, and velocity conditions. Using freestream boundary conditions, our results were plausible. In another category, we solved the linearized two-dimensional Euler equations to test the effectiveness of radiation boundary conditions. Here we utilized MAPLE to compute eigenvalues and eigenvectors of the Jacobian given variable and flux vectors. We experienced a minor problem with inflow and outflow boundary conditions. Next, we solved the quasi one dimensional unsteady flow equations with an incoming acoustic wave of amplitude 10(exp -6). The small amplitude sound wave was incident on a convergent-divergent nozzle. After finding a steady-state solution and then marching forward, our solution indicated that after 30 periods the acoustic wave had dissipated (a period is time required for sound wave to traverse one end of nozzle to other end).
Porter-Locklear, Freda↗
Evaluation of high order schemes for nonlinear wave computations
We present results of the workshop's benchmark problems of the category 2. This category of problems is designed to test the nonlinear wave propagation properties of a computational scheme. We chose three high order spatially accurate algorithms for our computations. These are the Dispersion- Relation- Preserving (DRP) scheme proposed by Tam and his colleagues, a fourth order extension of the MacCormack scheme proposed by Gottlieb and Turkel and an Essentially Non Oscillatory (ENO) scheme proposed by Shu and Osher.
Hayder, M. Ehtesham↗
A Theoretical and Observational Study of Large and Small-Scale Dynamics in the Mesosphere and Lower Thermosphere in Support of TIMED
The long-term objectives of this IDS component of the TIMED mission are to define, through a combination of modeling and data analysis efforts, the influences of large- and small-scale waves (tidal, planetary, and gravity waves) on the circulation, structure, composition, and variability of the mesosphere and lower thermosphere. Particular emphasis is aimed at the TIMED core science objectives of defining the structure and energetics of the TIMED core region, approx. 60 to 180 km. To do so, however, it is also essential to understand the dynamical influences and contributions because of their considerable direct and indirect influences on structure and energetics. To accomplish these goals, we anticipate two parallel modeling efforts and a significant data analysis effort following TIMED launch. The modeling efforts will address both: the residual circulation response to mean and variable wave forcing of the MLT through development of a spherical model addressing balanced flow dynamics and transience and a more comprehensive effort addressing gravity wave propagation, interactions, nonlinearity, and spectral evolution and transports in canonical and realistic environments. The data analysis effort is envisioned to involve application of ground-based measurements and TIMED data analyses to a quantification of gravity wave forcing and effects at one or more sites with comprehensive measurement suites and extension of the inferred forcing globally, based on distributed ground-based measurements. Research results and publications resulting from the research are included.
Fritts, David C.↗
WDM Component Requirements for Bit-Parallel Fiber Optic Computer Networks
The device specifications for an all optical bit-parallel WDM single fiber link for the cluster computer network community are intended for dissemination to the opto-electronic device research community to stimulate synergy between the two, ultimately leading to early availability of new devices to the computer network researchers.
wavelength↗
Study of nonlinear MHD equations governing the wave propagation in twisted coronal loops
The solar corona, modelled by a low beta, resistive plasma slab, sustains MHD wave propagations due to shearing footpoint motions in the photosphere. By using a numerical algorithm the excitation and nonlinear development of MHD waves in twisted coronal loops are studied. The plasma responds to the footpoint motion by sausage waves if there is no twist. The twist in the magnetic field of the loop destroys initially developed sausage-like wave modes and they become kinks. The transition from sausage to kink modes is analyzed. The twist brings about mode degradation producing high harmonics and this generates more complex fine structures. This can be attributed to several local extrema in the perturbed velocity profiles. The Alfven wave produces remnants of the ideal 1/x singularity both for zero and non-zero twist and this pseudo-singularity becomes less pronounced for larger twist. The effect of nonlinearity is clearly observed by changing the amplitude of the driver by one order of magnitude. The magnetosonic waves also exhibit smoothed remnants of ideal logarithmic singularities when the frequency of the driver is correctly chosen. This pseudo-singularity for fast waves is absent when the coronal loop does not undergo any twist but becomes pronounced when twist is included. On the contrary, it is observed for slow waves even if there is no twist. Increasing the twist leads to a higher heating rate of the loop. The larger twist shifts somewhat uniformly distributed heating to layers inside the slab corresponding to peaks in the magnetic field strength.
Parhi, S.↗
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↗
Non-linear propagation in near sonic flows
A nonlinear analysis is developed for sound propagation in a variable-area duct in which the mean flow approaches choking conditions. A quasi-one-dimensional model is used and the nonlinear analysis represents the acoustic disturbance as a sum of interacting harmonics. The numerical procedure is stable for cases of strong interaction and is able to integrate through the throat region without any numerical instability.
Nayfeh, A. H.↗