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At least 271 records · Page 15
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NASA NTRS1979

Proton-driven electromagnetic instabilities in high-speed solar wind streams

Electromagnetic instabilities of the field-aligned, right-hand circularly polarized magnetosonic wave and the left-hand circularly polarized Alfven wave driven by two drifted proton components are analyzed for model parameters determined from Imp 7 solar wind proton data measured during high-speed flow conditions. Growth rates calculated using bi-Lorentzian forms for the main and beam proton as well as core and halo electron velocity distributions do not differ significantly from those calculated using bi-Maxwellian forms. Using distribution parameters determined from 17 measured proton spectra, we show that considering the uncertainties the magnetosonic wave may be linearly stable and the Alfven wave is linearly unstable. Because proton velocity distribution function shapes are observed to persist for times long compared to the proton gyroperiod, the latter result suggests that linear stability theory fails for proton-driven ion cyclotron waves in the high-speed solar wind.

Abraham-Shrauner, B.↗
NASA NTRS1979

Lyapunov stability and its application to systems of ordinary differential equations

An outline and a brief introduction to some of the concepts and implications of Lyapunov stability theory are presented. Various aspects of the theory are illustrated by the inclusion of eight examples, including the Cartesian coordinate equations of the two-body problem, linear and nonlinear (Van der Pol's equation) oscillatory systems, and the linearized Kustaanheimo-Stiefel element equations for the unperturbed two-body problem.

Kennedy, E. W.↗
NASA NTRS1980

Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined.

El-Hady, N. M.↗
NASA NTRS1980

Status of linear boundary-layer stability and the e to the nth method, with emphasis on swept-wing applications

The-state-of-the-art for the application of linear stability theory and the e to the nth power method for transition prediction and laminar flow control design are summarized, with analyses of previously published low disturbance, swept wing data presented. For any set of transition data with similar stream distrubance levels and spectra, the e to the nth power method for estimating the beginning of transition works reasonably well; however, the value of n can vary significantly, depending upon variations in disturbance field or receptivity. Where disturbance levels are high, the values of n are appreciably below the usual average value of 9 to 10 obtained for relatively low disturbance levels. It is recommended that the design of laminar flow control systems be based on conservative estimates of n and that, in considering the values of n obtained from different analytical approaches or investigations, the designer explore the various assumptions which entered into the analyses.

Hefner, J. N.↗
NASA NTRS1979

Robustness properties of discrete time regulators, LOG regulators and hybrid systems

Robustness properites of sample-data LQ regulators are derived which show that these regulators have fundamentally inferior uncertainty tolerances when compared to their continuous-time counterparts. Results are also presented in stability theory, multivariable frequency domain analysis, LQG robustness, and mathematical representations of hybrid systems.

Stein, G.↗
NASA NTRS1980

Attitude stability of spinning satellites

Some problems of attitude stability of spinning satellites are treated in a rigorous manner. With certain restrictions, linearized stability analysis correctly predicts the attitude stability of spinning satellites, even in the critical cases of the Liapunov-Poincare stability theory.

Caughey, T. K.↗
NASA NTRS1980

The radiation of sound by the instability waves of a compressible plane turbulent shear layer

The problem of acoustic radiation generated by instability waves of a compressible plane turbulent shear layer is solved. The solution provided is valid up to the acoustic far-field region. It represents a significant improvement over the solution obtained by classical hydrodynamic-stability theory which is essentially a local solution with the acoustic radiation suppressed. The basic instability-wave solution which is valid in the shear layer and the near-field region is constructed in terms of an asymptotic expansion using the method of multiple scales. This solution accounts for the effects of the slightly divergent mean flow. It is shown that the multiple-scales asymptotic expansion is not uniformly valid far from the shear layer. Continuation of this solution into the entire upper half-plane is described. The extended solution enables the near- and far-field pressure fluctuations associated with the instability wave to be determined. Numerical results show that the directivity pattern of acoustic radiation into the stationary medium peaks at 20 degrees to the axis of the shear layer in the downstream direction for supersonic flows. This agrees qualitatively with the observed noise-directivity patterns of supersonic jets.

Tam, C. K. W.↗
NASA NTRS1980

Experimental analysis of the boundary layer transition with zero and positive pressure gradient

The influence of a positive pressure gradient on the boundary layer transition is studied. The mean velocity and turbulence profiles of four cases are examined. As the intensity of the pressure gradient is increased, the Reynolds number of the transition onset and the length of the transition region are reduced. The Tollmein-Schlichting waves disturb the laminar regime; the amplification of these waves is in good agreement with the stability theory. The three dimensional deformation of the waves leads finally to the appearance of turbulence. In the case of zero pressure gradient, the properties of the turbulent spots are studied by conditional sampling of the hot-wire signal; in the case of positive pressure gradient, the turbulence appears in a progressive manner and the turbulent spots are much more difficult to characterize.

Arnal, D.↗
NASA NTRS1980

Free-stream disturbances, continuous eigenfunctions, boundary-layer instability and transition

A rational foundation is provided for the application of the linear stability theory of parallel shear flows to transition prediction. An explicit method is given for carrying out the necessary calculations. The expansions are shown to be complete. Sample calculations show that a typical boundary layer is very sensitive to vorticity disturbance in the inner boundary layer near the critical layer. Vorticity disturbances three or four boundary layer thicknesses above the boundary are nearly uncoupled from the boundary layer, in that the amplitudes of the discrete Tollmein-Schlichting waves are an extremely small fraction of the amplitude of the disturbance.

Salwen, H.↗
NASA NTRS1981

Compressible boundary-layer stability calculations for sweptback wings with suction

The stability of the laminar boundary layers on two transonic wings of infinite span with distributed suction is investigated with the compressible, parallel-flow stability theory. Both wings have supercritical airfoil sections; one has a sweep angle of 23 deg, the other of 35 deg. Zero-frequency disturbances are used to represent cross-flow instability, and disturbances with the wavenumber vector aligned with the local flow direction represent traveling-wave instability. In both cases, the maximum spatial amplification rate is used as a measure of the instability. For the suction, distributions with constant mass flux downstream of the starting point are used. The main objective is to determine how the maximum amplification rate varies with the magnitude and starting point of the suction. It is found for both types of disturbances that the maximum amplification rate varies almost linearly with the suction magnitude up to at least the point where the amplification rate is halved. Different starting locations for the suction in the first 4% of the chord were found to affect cross-flow instability, but to have little influence on traveling-wave instability.

Mack, L. M.↗
NASA NTRS1981

Wave-particle transport by weak electrostatic flow shear fluctuations

A description is presented of the first consistent theoretical treatment of transport due to weak electrostatic fluctuations from microinstabilities driven by a shear in plasma flow parallel to a uniform magnetic field. The model used considers electrostatic fluctuations in a Vlasov plasma with sheared bulk velocity parallel to a uniform magnetic field. The linear stability theory for the model has been studied by Gary and Schwartz (1980). In the current investigation, a calculation is performed of the wave-particle transport associated with the electrostatic flow shear instability.

Gary, S. P.↗
NASA NTRS1982

Experiments on the flow and acoustic properties of a moderate-Reynolds-number supersonic jet

Flow and acoustic properties of a jet at Reynolds number of 70,000 were studied at Mach 2.1. Measurements in a free jet test facility were made with pitot tubes and hot-wire anemometry. Center-line Mach number distributions for natural and excited jets were obtained. A slow initial growth rate was in the potential core region of the jet, indicating a transition from laminar to turbulent flow in moderate Reynolds number jets. The transition occurred within the first 2-3 diameters. Spectral components were calculated for the fluctuating flowfield, and sound pressure levels were measured for the overall near-field noise. The centroid of noise was located about 8 nozzle diameters downstream. The growth rates of instabilities were determined to be in agreement with linear stability theory predictions over a broad frequency range.

Troutt, T. R.↗
NASA NTRS1982

Generation of the auroral kilometric radiation

Data collected from the S3-3 spacecraft in the auroral kilometric radiation (AKR) source region are employed to form a stability theory from which numerical results are obtained and discussed. The distribution function was found to be isotropic outside the auroral atmospheric loss-cone region, which was partially filled with upcoming electrons. A parallel electric field was observed to be modifying the loss-cone distribution. A model distribution function is formulated, along with a magnetic field model expressed in terms of the electron cyclotron frequency. Models for the parallel electric field are also introduced, the first with the field distributed over a broad altitude range, while the second assumes a potential drop only above 4000 km. The presence of the field is found to enhance the growth rate of the AKR. At higher altitudes, the cutoff frequency of the X mode is affected by the rising energetic electrons. Finally, the folding distances of spatial amplification are calculated.

Wu, C. S.↗
NASA NTRS1983

Convection effects at solid-liquid interfaces: Influence of gravity

The stability of the flow between two vertical, infinite, rigid, coaxial cylinders held at different temperatures is analyzed by linear stability theory. For a Prandtl number of 22.8 and a radius ratio of 0.02, the flow is unstable to an axisymmetric perturbation at a critical Grashof number of 2150; the wave speed of the instability is comparable to the maximum velocity of the unperturbed flow. When the rigid outer cylinder-fluid interface is replaced by a crystal-melt interface which can change shape, two new modes of instability occur at lower Grashof numbers.

Glicksman, M. E.↗
NASA NTRS1982

The development of a two-dimensional wavepacket in a growing boundary layer

The evolution of a two-dimensional wavepacket in a growing boundary layer is discussed in terms of linear stability theory. The wavepacket is represented by an integral of periodic wavetrains, each of which is defined as a series in terms of the inverse of the local displacement thickness Reynolds number to the one half power. Comparisons are made between the waveforms computed directly from the integral, a steepest-descent expansion of the integral, and a global expansion about the peak of the wavepacket.

Gaster, M.↗
NASA NTRS1983

On the interaction of a sound pulse with the shear layer of an axisymmetric jet. II - Heated jets

The fluctuating field of a heated jet excited by a sound pulse is simulated numerically. The fluctuations in both the flow field and the far field are studied. The flow field results depend crucially on the stability properties of the heated jet. The altered stability properties due to the heating cause a reduction in the overall fluctuations and a shift of the instability waves into lower frequencies. These changes cause a similar downward shift in the far field spectrum and a reduction in the total far field noise. The results provide a partial explanation in terms of stability theory of experimentally observed properties of the noise of heated jets.

Bayliss, A.↗
NASA NTRS1983

Stability experiments in rotating-disk flow

An experimental study of the transitional flow on a flat disk, rotating in still air, has been conducted. Using digitized hot-wire data, the axes of the stationary spiral vortices, which are the primary instability mechanism for the disk flow, have been mapped-out in terms of both spatial coordinates and velocity fluctuations. Data are presented for a clean disk and for a disk with a single, isolated roughness element. The data show that the disk vortices are generated at discrete roughness disturbance sites on the disk and that they propagate and grow as wave packets. The familiar vortex pattern of 30 or so vortices results only when these wave packets have merged and filled the entire circumference. The appearance of stationary, secondary vortices prior to turbulent breakdown has also been observed. Comparisons with linear stability theory show reasonable agreement with measured growth rate data.

Wilkinson, S. P.↗