Nonlinear actuator disk theory and flow field calculations, including nonuniform loading
Actuator disk theory and flow field calculations for propeller induced flow with nonuniform circulation distribution
Greenberg, M. D.↗
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Observations of enhanced ion line frequency spectrum during Arecibo ionospheric modification experiment
The Arecibo 430 MHz incoherent scatter radar (ISR) was used to monitor the effects of modifying the ionosphere by a high power HF transmitter feeding the 305 m reflector antenna. When in the ordinary magnetoionic mode parametric instabilities develop in the ionosphere near the reflection level. Manifestations of these instabilities are the strong enhancement of Langmuir oscillations in the direction of the ISR beam at a wavelength of 35 cm and the simultaneous much weaker enhancement of ion oscillations in that direction. The spectral analysis of the enhanced peak with a height resolution of 2.4 km shows that the ionic mode enhancement most often has a double humped frequency spectrum corresponding to up- and down-going ion acoustic waves. The shape of the frequency spectrum is interpreted in terms of a stable oscillation which is driven by a secondary electrostatic field caused by nonlinear interaction of Langmuir waves within a cone centered on the magnetic field and by the scattering of the pump field on stable Langmuir waves travelling along the direction of the ISR.
Hagfors, T.↗
Nonlinear analysis of generalized cross-field current instability
Analysis of the generalized cross-field current instability is carried out in which cross-field drift of both the ions and electrons and their temperatures are permitted to vary in time. The unstable mode under consideration is the electromagnetic generalization of the classical modified-two-stream instability. The generalized instability is made of the modified-two-stream and ion-Weibel modes. The relative importance of the features associated with the ion-Weibel mode and those of the modified-two-stream mode is assessed. Specific applications are made to the Earth's neutral sheet prior to substorm onset and to the Earth's bow shock. The numerical solution indicates that the ion-Weibel mode dominates in the Earth's neutral sheet environment. In contrast, the situation for the bow shock is dominated by the modified-two-stream mode. Notable differences are found between the present calculation and previous results on ion-Weibel mode which restrict the analysis to only parallel propagating waves. However, in the case of Earth's bow shock for which the ion-Weibel mode plays no important role, the inclusion of the electromagnetic ion response is found to differ little from the previous results which treats ions responding only to the electrostatic component of the excited waves.
Yoon, Peter H.↗
Nonlinear Bubble Interactions in Acoustic Pressure Fields
The systems consisting of a two-phase mixture, as clouds of bubbles or drops, have shown many common features in their responses to different external force fields. One of particular interest is the effect of an unsteady pressure field applied to these systems, case in which the coupling of the vibrations induced in two neighboring components (two drops or two bubbles) may result in an interaction force between them. This behavior was explained by Bjerknes by postulating that every body that is moving in an accelerating fluid is subjected to a 'kinetic buoyancy' equal with the product of the acceleration of the fluid multiplied by the mass of the fluid displaced by the body. The external sound wave applied to a system of drops/bubbles triggers secondary sound waves from each component of the system. These secondary pressure fields integrated over the surface of the neighboring drop/bubble may result in a force additional to the effect of the primary sound wave on each component of the system. In certain conditions, the magnitude of these secondary forces may result in significant changes in the dynamics of each component, thus in the behavior of the entire system. In a system containing bubbles, the sound wave radiated by one bubble at the location of a neighboring one is dominated by the volume oscillation mode and its effects can be important for a large range of frequencies. The interaction forces in a system consisting of drops are much smaller than those consisting of bubbles. Therefore, as a first step towards the understanding of the drop-drop interaction subject to external pressure fluctuations, it is more convenient to study the bubble interactions. This paper presents experimental results and theoretical predictions concerning the interaction and the motion of two levitated air bubbles in water in the presence of an acoustic field at high frequencies (22-23 KHz).
Barbat, Tiberiu↗
Squeezing spectra for nonlinear optical systems
The squeezing spectra for the output fields of several intracavity nonlinear optical systems are obtained. It is shown that at critical points, e.g., the turning points for optical bistability, the threshold for parametric oscillation, and the self-pulsing instability in second-harmonic generation, perfect squeezing in the output field is, in principle, possible.
Collett, M. J.↗
Computation of supersonic flow fields about bodies in coning motion using a shock-capturing finite-difference technique.
A numerical method for computing the nonlinear inviscid flow field surrounding a body performing coning motion is described. The method permits accurate computation of the aerodynamic moment due to one of the four motions characterizing an arbitrary nonplanar motion. Results of computations for a slender circular cone in coning motion are presented, and show good agreement with experiment for angles of attack up to twice the cone half angle. The computational results display significant departure of the side moment from the linear theory value with increasing angle of attack, but agree well with experimental measurements. This indicates that the initial nonlinear behavior of the aerodynamic moment is determined primarily by the inviscid flow.
Schiff, L. B.↗
The nonlinear breakup of the sun's toroidal field
There are good reasons for believing that the sun has a strong toroidal magnetic field in the stably stratified region of convective overshoot sandwiched between the radiative zone and convective zone proper. The magnetic field in this region is modeled by studying the behavior of a layer of uniform field embedded in a subadiabatic atmosphere. Since the field can support extra mass, such a configuration is top-heavy, and instabilities of the Rayleigh-Taylor type can occur. Numerical integration of the two-dimensional compressible MHD equations makes it possible to follow the evolution of this instability into the nonlinear regime. The initial buoyancy-driven instability of the magnetic field gives rise to strong shearing motions, thereby exciting secondary Kelvin-Helmholtz instabilities which wrap the gas into regions of intense vorticity. The somewhat surprising subsequent motions are determined primarily by the strong interactions between vortices.
Hughes, D. W.↗
Computer simulation of the velocity diffusion of cosmic rays
Monte Carlo simulation experiments were performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitable chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory.
Kaiser, T. B.↗
Computer simulation of the velocity diffusion of cosmic rays
Monte Carlo simulation experiments have been performed in order to study the velocity diffusion of charged particles in a static turbulent magnetic field. By following orbits of particles moving in a large ensemble of random magnetic field realizations with suitably chosen statistical properties, a pitch-angle diffusion coefficient is derived. Results are presented for a variety of particle rigidities and rms random field strengths and compared with the predictions of standard quasi-linear theory and the nonlinear partially averaged field theory.
Kaiser, T. B.↗
Generation of large-scale density fluctuations by buoyancy
The generation of fluid motion from a state of rest by buoyancy forces acting on a homogeneous isotropic small-scale density field is considered. Nonlinear interactions between the generated fluid motion and the initial isotropic small-scale density field are found to create an anisotropic large-scale density field with spectrum proportional to kappa(exp 4). This large-scale density field is observed to result in an increasing Reynolds number of the fluid turbulence in its final period of decay.
Chasnov, J. R.↗
Linear velocity fields in non-Gaussian models for large-scale structure
Linear velocity fields in two types of physically motivated non-Gaussian models are examined for large-scale structure: seed models, in which the density field is a convolution of a density profile with a distribution of points, and local non-Gaussian fields, derived from a local nonlinear transformation on a Gaussian field. The distribution of a single component of the velocity is derived for seed models with randomly distributed seeds, and these results are applied to the seeded hot dark matter model and the global texture model with cold dark matter. An expression for the distribution of a single component of the velocity in arbitrary local non-Gaussian models is given, and these results are applied to such fields with chi-squared and lognormal distributions. It is shown that all seed models with randomly distributed seeds and all local non-Guassian models have single-component velocity distributions with positive kurtosis.
Scherrer, Robert J.↗
HF-induced parametric decay in presence of field-aligned irregularities
A nonlinear theory for the saturation of the HF-induced parametric decay instability is formulated in terms of the normal modes of a field-aligned plasma wave duct. Coupling coefficients between modes are derived, and a saturation spectrum is computed numerically for a typical irregularity. The computed spectrum shows that unstable waves may propagate at larger angles to the magnetic field than would be the case in a regular medium. The relevance of this work to the experiment of Muldrew and Showen (1977), concerning the height of the HF-induced plasma line at Arecibo, is discussed. A possible explanation is also found for the 'decay line' feature in comparison with the 'broad bump' in the observed backscatter spectrum.
Rypdal, K.↗
A study of the mechanism of internal gravity wave generation by quasigeostrophic meteorological motions
Numerous experiments on the detection of atmospheric waves in the frequency range from acoustic to planetary at meteor heights have revealed that important wave sources are meteorological processes in the troposphere (cyclones, atmospheric fronts, jet streams, etc.). A dynamical theory based on the others work include describing the adaptation of meteorological fields to the geostropic equilibrium state. According to this theory, wave motions appear as a result of constant competition between the maladjustment of the wind and pressure fields due to nonlinear effects and the tendency of the atmosphere to establish a quasi-geostrophic equilibrium of these fields. These meteorological fields are discussed.
Medvedev, A. S.↗
High speed turboprop aeroacoustic study (single rotation). Volume 1: Model development
A frequency-domain noncompact-source theory for the steady loading and volume-displacement (thickness) noise of high speed propellers has been developed and programmed. Both near field and far field effects have been considered. The code utilizes blade surface pressure distributions obtained from three-dimensional nonlinear aerodynamic flow field analysis programs as input for evaluating the steady loading noise. Simplified mathematical models of the velocity fields induced at the propeller disk by nearby wing and fuselage surfaces and by angle-of-attack operation have been developed to provide estimates of the unsteady loading imposed on the propeller by these potential field type interactions. These unsteady blade loadings have been coupled to a chordwise compact propeller unsteady loading noise model to provide predictions of unsteady loading noise caused by these installation effects. Finally, an analysis to estimate the corrections to be applied to the free-field noise predictions in order to arrive at the measurable fuselage sound pressure levels has been formulated and programmed. This analysis considers the effects of fuselage surface reflection and diffraction together with surface boundary layer refraction. The steady loading and thickness model and the unsteady loading model have been verified using NASA-supplied data for the SR-2 and SR-3 model propfans. In addition, the steady loading and thickness model has been compared with data from the SR-6 model propfan. These theoretical models have been employed in the evaluation of the SR-7 powered Gulfstream aircraft in terms of noise characteristics at representative takeoff, cruise, and approach operating conditions. In all cases, agreement between theory and experiment is encouraging.
Whitfield, C. E.↗
A stability criterion for steady finite amplitude convection with an external magnetic field.
Convection and stability criteria for nonlinear steady solutions with homogeneous vertical magnetic field acting on fluid
FLOW EQUATION↗
Constraints on geomagnetic secular variation modeling from electromagnetism and fluid dynamics of the Earth's core
A spherical harmonic representation of the geomagnetic field and its secular variation for epoch 1980, designated GSFC(9/84), is derived and evaluated. At three epochs (1977.5, 1980.0, 1982.5) this model incorporates conservation of magnetic flux through five selected patches of area on the core/mantle boundary bounded by the zero contours of vertical magnetic field. These fifteen nonlinear constraints are included like data in an iterative least squares parameter estimation procedure that starts with the recently derived unconstrained field model GSFC (12/83). Convergence is approached within three iterations. The constrained model is evaluated by comparing its predictive capability outside the time span of its data, in terms of residuals at magnetic observatories, with that for the unconstrained model.
Benton, E. R.↗
Simulation of Supersonic Jet Noise with the Adaptation of Overflow CFD Code and Kirchhoff Surface Integral
An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.
Kandula, Max↗
Simulation of Jet Noise with OVERFLOW CFD Code and Kirchhoff Surface Integral
An acoustic prediction capability for supersonic axisymmetric jets was developed on the basis of OVERFLOW Navier-Stokes CFD (Computational Fluid Dynamics) code of NASA Langley Research Center. Reynolds-averaged turbulent stresses in the flow field are modeled with the aid of Spalart-Allmaras one-equation turbulence model. Appropriate acoustic and outflow boundary conditions were implemented to compute time-dependent acoustic pressure in the nonlinear source-field. Based on the specification of acoustic pressure, its temporal and normal derivatives on the Kirchhoff surface, the near-field and the far-field sound pressure levels are computed via Kirchhoff surface integral, with the Kirchhoff surface chosen to enclose the nonlinear sound source region described by the CFD code. The methods are validated by a comparison of the predictions of sound pressure levels with the available data for an axisymmetric turbulent supersonic (Mach 2) perfectly expanded jet.
Kandula, M.↗