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Three-dimensional linear secondary instability theory is extended for compressible boundary layers on a flat plate in the presence of finite amplitude Tollmien-Schlichting (T-S) waves. The focus is on principal parametric resonance responsible for the strong growth of harmonics in a low disturbance environment.
An adaptive grid generator for adaptive node movement is here derived by combining a variational formulation of Winslow's (1981) variable-diffusion method with a directional control functional. By applying harmonic-function theory, it becomes possible to define conditions under which there exist unique solutions of the resulting elliptic equations. The results obtained for the grid generator's application to the complex problem posed by the fluid instability-driven magnetic field reconnection demonstrate one-tenth the computational cost of either a Eulerian grid or an adaptive grid without directional control.
Thermoacoustic instabilities in annular or circular combustors are often coupled with azimuthal modes. These modes can be characterized by a spin ratio (SR), which quantifies the dominant mode between two counter-rotating waves, and a phase difference between them, which is directly related to the orientation of the antinodal line. This study investigates the instability amplitudes, SR, and phase difference of two closely spaced (3% of their mean frequency), yet distinct azimuthal modes; one is the first azimuthal (1A) mode, and the other is a combination of first azimuthal and first longitudinal (1A1L) mode. Each mode itself consists of two peaks that are spaced even more closely in frequency (0.8%). Furthermore, distinct harmonics at 2× and 3× of these frequencies, presumably associated with nonlinearities, are also evident in the spectra. Each mode is bandpass filtered in spectrum to analyze them separately. For the 1A mode, the SR and phase difference exhibit a variety of behaviors—including quasi-periodic standing waves, spinning waves, and intermittency—depending on operating conditions such as thermal power and azimuthal fuel staging. Similar trends are observed for the 1A1 L mode. Moreover, there is clear coupling between the 1A and 1A1 L modes, as their SRs are almost synchronized during the quasi-periodic standing wave. This synchronization is observed in phase differences as well, but not in the instability amplitude. For spinning dominant wave conditions, the SRs of each mode have similar average values, but they fluctuate in a seemingly random fashion. For the phase difference, both average and fluctuation are not correlated. In contrast, the instability amplitudes are strongly correlated, with modulation of the 1A mode leading to that of the 1A1 L mode. Furthermore, these results clearly indicate that complex coupling occurs across closely spaced frequencies under instability conditions, coupling that must be understood in order to capture limit cycle dynamics.
Destabilization of ion cyclotron waves—waves with frequencies close to ion cyclotron harmonics—in inhomogeneous plasmas with Maxwell velocity distribution is considered. A new mechanism of destabilization of these waves is found, whereas the known interaction between cyclotron waves and drift waves is shown to be hardly able to lead to instabilities in realistic tokamak plasmas. Our finding is that the resonance wave–particle interaction in the presence of temperature gradient can change the diamagnetic drift frequency in such a way that the destabilizing influence of the diamagnetic drift exceeds Landau damping. This occurs when the energy of resonance particles is sufficiently high, which is always the case due to the infinite tail of the Maxwell distribution. Particles with higher energies provide a larger ratio of drive to damping, but the number of resonance particles and, thus, instability growth rates are exponentially small when particle energy is very high. Therefore, only moderately suprathermal particles can lead to observable instabilities. A condition for instabilities driven by these particles is obtained. Destabilization of electrostatic cyclotron waves and ordinary cyclotron waves is studied.
Compositional fluctuations of the binary alloy result in the corresponding fluctuations of the thermal conductivity of the material. During crystal growth, these fluctuations can significantly modify the local temperature fields at the liquid-solid interface. This, in turn, will affect the morphological stability of the growing interface. In this work, the temperature dependence of the thermal conductivity of the solid phase has been included into the Mullins-Sekerka formalism. A significant effect on the onset of the instability of planar interface has been predicted. It has been found, in particular, that for binary systems with the segregation coefficient above unity a flat interface is always unstable. The shape of the interface fluctuation should have a single harmonic character with a well defined wavelength.
We show that, although nonlinear optics may give rise to a vast multitude of statistics, all these statistics converge, in their extreme-value limit, to one of a few universal extreme-value statistics. Specifically, in the class of polynomial nonlinearities, such as those found in the Kerr effect, weak-field harmonic generation, and multiphoton ionization, the statistics of the nonlinear-optical output converges, in the extreme-value limit, to the exponentially tailed, Gumbel distribution. Exponentially growing nonlinear signals, on the other hand, such as those induced by parametric instabilities and stimulated scattering, are shown to reach their extreme-value limits in the class of the Fréchet statistics, giving rise to extreme-value distributions (EVDs) with heavy, manifestly nonexponential tails, thus favoring extreme-event outcomes and rogue-wave buildup.
Many plasma-wave phenomena, observed by space-borne radio sounders, cannot be properly explained in terms of wave propagation in a cold plasma consisting of mobile electrons and infinitely massive positive ions. These phenomena include signals known as plasma resonances. The principal resonances at the harmonics of the electron cyclotron frequency, the plasma frequency, and the upper-hybrid frequency are well explained by the warm-plasma propagation of sounder-generated electrostatic waves, Other resonances have been attributed to sounder-stimulated plasma instability and non-linear effects, eigenmodes of cylindrical electromagnetic plasma oscillations, and plasma memory processes. Data from the topside sounders of the International Satellites for Ionospheric Studies (ISIS) program played a major role in these interpretations. A data transformation and preservation effort at the Goddard Space Flight Center has produced digital ISIS topside ionograms and a metadata search program that has enabled some recent discoveries pertaining to the physics of these plasma resonances. For example, data records were obtained that enabled the long-standing question (several decades) of the origin of the plasma resonance at the fundamental electron cyclotron frequency to be explained [Muldrew, Radio Sci., 2006]. These data-search capabilities, and the science enabled by them, will be presented as a guide to desired data search capabilities to be included in the Virtual Wave Observatory (VWO).
The magnetospheric compression associated with the very large magnetic storm of August 4-5, 1972, provided an opportunity for Explorer 45 to observe plasma waves in the magnetosphere and the magnetosheath during extremely disturbed conditions. Electrostatic noise bursts were observed near the plasmapause in electric-field channels from 35 Hz to 5.62 kHz. In the outer magnetosphere, electric-field noise bands apparently harmonically related to the electron gyrofrequency with components as low as 3 kHz and as high as 50 kHz were observed. The electric field of the fundamental was perpendicular to the magnetic-field vector. A mechanism including the electron cyclotron instability may generate the noise band. Hiss of 100-1000 Hz was observed in the outer magnetosphere. The electromagnetic hiss was generally weak and was observed in the magnetic wide-band data only when it was strong. In the magnetosheath broad band, incoherent noise (hiss) was observed from 1 Hz to 100 kHz. This magnetosheath hiss was the strongest phenomenon observed by the plasma-wave detectors during the lifetime of Explorer 45. The highest intensities of magnetosheath hiss occurred at the magnetopause. Its broad-band nature suggests that magnetosheath hiss was generated locally. Broad-band noise bursts and short bursts of chorus were also observed in the magnetosheath.
Transonic testing of an NACA 64A010 airfoil at the Ohio State University Aero-Astro Research Laboratory is described, and results of fixed angle of attack and pitch oscillation experiments are discussed. The operating range was Mach 0.20 to 1.07 with available total pressures of 140,000 N/m2 to 620,000 N/m2. The airfoil model was mounted on roller bearings installed in the solid sidewalls of the tunnel test section. The equipment included transducers to measure unsteady pressures, and static pressure taps obtaining steady-state data. The data gathered at Mach 0.8 gave an indication of the influence of the natural shock instability and shock-induced flow separation on the unsteady pressures, with the location of the peak disturbance level shifting forward in the comparison of 0 to 2 deg pitch angle data. The oscillating airfoil data is examined in terms of harmonic content and the in-phase and out-of-phase components. It is concluded that the experimental data has good qualitative comparison with methods accounting for shock interaction.
Under controlled small-amplitude excitation, an initially laminar free shear layer experiences maximum growth rate at a Strouhal number St(theta) of 0.017 (consistent with theory) and maximum growth at St(theta) = 0.011, while the natural instability frequency St(theta-n) (of an unexcited shear layer) is found to have an intermediate value. Investigations in both axisymmetric and plane shear layers in a number of independent facilities reveal that the St(theta-n) value falls in the range 0.0125-0.0155, depending on the exit boundary-layer fluctuation level and the spanwise radius of curvature. The St(theta-n) value decreases with increasing jet diameter or exit boundary-layer fluctuation level, but is not a direct function of the exit momentum thickness Reynolds number. For a given facility, the instability details are found to be independent of whether the entrainment at the lip is parallel to the stream or orthogonal (due to the addition of an end plate). The steamwise evolutions of the amplitudes at the fundamental frequency and its harmonics and subharmonics are unique functions of the downstream distance nondimensionalized by the exit momentum thickness, but their details remain functions of the flow geometry (i.e., axisymmetric or plane).
This paper presents experimental data taken in the forward region of a separated internal free-shear layer produced in an internal cavity flowfield. It has been found that in the region very near the forward restrictor, experimental velocity profiles agree closely with the exact Stuart instability velocity profile with various values of a steepness parameter. Reynolds shear-stress profiles suggest the presence of counter-rotating longitudinal vortices. Spectral analysis by the maximum entropy method of the time samples within the vortices indicates subharmonic and harmonic components of the fundamental frequency, with a weak indication of the fundamental frequency itself.
A report describing the operating principles of hollow-cathode-based plasma contactors emitting or collecting electrons from an ambient plasma is summarized. Preliminary experiments conducted to determine the noise generated by these plasma contactors in the emission-current return line and in the plasma near it are described. These noise data are measured as current fluctuations in the return line and to the Langmuir probe and then analyzed using a fast Fourier transform technique. The spectral compositions of the data are characterized using power spectral density plots which are examined to identify possible noise source(s) and production mechanism(s). The precautions taken in the construction and calibration of the instrumentation to assure adequate frequency response are described. Experimental results show that line-current noise levels are typically 2 percent of the electron current being emitted or collected. However, noise levels increase to as much as 20 percent of the electron current at a few electron-collection operating conditions. The frequencies associated with most of the noise were harmonics of the 60 Hz input to system power supplies. Plasma noise had characteristics similar in magnitude and frequency to those for the return-line noise, but they contained additional features at frequencies considered to be related to ion-acoustic instabilities. Also discussed is a new probe positioning system built to facilitate future plasma-contractor research.
Satellite observations in the auroral plasma have revealed that extremely low frequency (ELF) waves play a dominant role in the acceleration of electrons and ions in the auroral plasma. The electromagnetic components of the ELF (EMELF) waves are the electromagnetic ion cyclotron (EMIC) waves below the cyclotron frequency of the lightest ion species in a multi-ion plasma. Shear Alfv6n waves (SAWS) constitute the lowest frequency components of the ELF waves below the ion cyclotron frequency of the heaviest ion. The -2 mechanism for the transfer of energy from such EMELF waves to ions affecting transverse ion heating still remains a matter of debate. A very ubiquitous fe8ture of ELF waves now observed in several rocket and satellite experiments is that they occur in conjunction with high-frequency electrostatic waves. The frequency spectrum of the composite wave turbulence extends from the low frequency of the Alfvenic waves to the high frequency of proton plasma frequency and/or the lower hybrid frequency. The spectrum does not show any feature organized by the ion cyclotron frequencies and their harmonics. Such broadband waves consisting of both the EM and ES waves are now popularly referred as BBELF waves. We present results here from 2.5-D particle-in-cell simulations showing that the ES components are directly generated by cross- field plasma instabilities driven by the drifts of the ions and electrons in the EM component of the BBELF waves.
Resonances of high energy particles in magnetic confinement devices due to electromagnetic instabilities can strongly modify the distribution, leading to a reduction in fusion power and even discharge termination and particle loss to the device walls through avalanche. The existence of a mode particle resonance depends on properties of the equilibrium, particle trajectories, and perturbation mode harmonic content. Resonance location is a function of particle energy and equilibrium field line helicity. Different methods for finding resonance location and energy dependence are developed. The properties of resonances are discussed using examples from magnetic fusion devices. Here, we show that if mode resonances exist at low particle energy, they very likely also exist at high energy, thus modifying high energy beam particles and fusion products. It is possible for a resonance to appear due to mode induced orbit helicity modification when it is forbidden at low mode amplitude.
The results of a new investigation of microbursts at meter-decameter wavelengths are reported. Several properties of microbursts reported earlier are confirmed, and some new properties, such as time profile characteristics, flux density, and energy spectra are studied in order to compare the properties of microbursts with those of normal type III bursts. Electron beams of similar characteristics are found to generate both microbursts and type III bursts. Plasma waves generated by the electron beams due to beam-plasma instability are quickly isotropized as they scatter on the density fluctuations in the corona, leading to the low brightness temperature of microbursts. The resulting low levels of plasma waves produce transverse radiation of low brightness temperature. As a result of the isotropization, the second harmonic plasma emission dominates the fundamental, so that microbursts are expected to be primarily a harmonic plasma emission.
The development of Gortler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion whilst the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflection character as the flow moves downstream. The latter result suggests that the major effect of Gortler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.
The development of Goertler vortices in boundary layers over curved walls in the nonlinear regime is investigated. The growth of the boundary layer makes a parallel flow analysis impossible except in the high wavenumber regime so in general the instability equations must be integrated numerically. Here the spanwise dependence of the basic flow is described using Fourier series expansion while the normal and streamwise variations are taken into account using finite differences. The calculations suggest that a given disturbance imposed at some position along the wall will eventually reach a local equilibrium state essentially independent of the initial conditions. In fact, the equilibrium state reached is qualitatively similar to the large amplitude high wave-number solution described asymptotically by Hall (1982). In general, it is found that the nonlinear interactions are dominated by a mean field type of interaction between the mean flow and the fundamental. Thus, even though higher harmonics of the fundamental are necessarily generated, most of the disturbance energy is confined to the mean flow correction and the fundamental. A major result of the calculations is finding that the downstream velocity field develops a strongly inflectional character as the flow moves downstream. The latter result suggests that the major effect of Goertler vortices on boundary layers of practical importance might be to make them highly receptive to rapidly growing Rayleigh modes of instability.
An unexpected occurrence following the second lithium release by the AMPTE-IRM spacecraft in the solar wind on September 20, 1984, was the appearance of electron cyclotron harmonic emissions. These emissions began about 50 s after the release and continued for several minutes. Narrow-band emissions polarized perpendicular to the magnetic field with amplitudes of approximately 0.00001 V/m were observed in each of the first five harmonic bands. The diffuse emissions extended from below the lowest measured frequency channel to above the highest narrow-band emission with a maximum below the electron cyclotron frequency. It will be shown that these observations are inconsistent with their generation by several ion beam instabilities.