Some nonlinear aspects of drift instabilities
Drift wave instabilities nonlinearities, discussing plasma growth rate and saturation coefficients, damping rate as function of amplitude and lower mode modification
Hai, F.↗
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Instability Wave-Streak Interactions in a Supersonic Boundary Layer
Optimal initial conditions for transient growth in a two-dimensional boundary layer flow correspond to stationary, counter-rotating vortices that subsequently develop into streamwise elongated streaks, which are characterized by an alternating pattern of low and high streamwise velocity. For incompressible flows, previous studies have shown that boundary layer modulation due to streaks below a threshold amplitude level can stabilize the Tollmien-Schlichting instability waves, resulting in a delay in the onset of laminar-turbulent transition. In the supersonic regime, the linearly, most-amplified waves become three-dimensional, corresponding to oblique, first-mode waves. This change in the character of dominant instabilities leads to an important change in the transition process, which is now dominated by oblique breakdown via nonlinear interactions between pairs of first-mode waves that propagate at equal but opposite angles with respect to the free stream. Because the oblique breakdown process is characterized by a rapid amplification of stationary streamwise streaks, artificial excitation of such streaks may be expected to promote transition in a supersonic boundary layer. Indeed, suppression of those streaks has been shown to delay the onset of transition in prior literature. Consistent with those findings, the present study shows that optimally growing stationary streaks indeed destabilize the first-mode waves, but only when the spanwise wavelength of the instability waves is equal to or smaller than twice the streak spacing. Transition in a benign disturbance environment typically involves first-mode waves with significantly longer spanwise wavelengths, and hence, these waves are stabilized by the optimal growth streaks. Thus, as long as the amplification factors for the destabilized, short wavelength instability waves remain below the threshold level for transition, a significant net stabilization is achieved, yielding a transition delay that is comparable to the length of the laminar region in the uncontrolled case.
Boundary layer transition↗
Ion-wave current instabilities and anomalous resistivity.
A theory of ion-wave current instabilities which takes into account, in a self-consistent manner, the inhomogeneities generated by field-aligned currents in a collisionless plasma is presented. Diamagnetic current associated with the current-produced density gradient is included in the distribution. The theory predicts that for a given frequency, the current threshold for ion-wave current instabilities is, in general, much below the threshold of ion acoustic instability in a uniform plasma as given by Fried and Gould. The current threshold is essentially zero in the limit when the ion Landau damping effect is negligible, or equivalently, the ion-wave current instabilities are absolute if there are no limitations on the wavelength. This is true even in the absence of externally applied density gradients in contrast to Kadomtsev's drift-wave results. For dimensions of interest in laboratory plasmas, the predicted linear growth rate increases with increasing longitudinal wavelength and with decreasing wavelength parallel to the diamagnetic current. Under the conditions of an experiment on anomalous resistivity (the dimensions but not the geometry of the machine have been considered), there is good agreement between the predicted onset of ion-wave current instabilities and the experimental data on the onset of anomalous resistivity.
Kan, J. R.↗
Screech tones from free and ducted supersonic jets
It is well known that screech tones from supersonic jets are generated by a feedback loop. The loop consists of three main components. They are the downstream propagating instability wave, the shock cell structure in the jet plume, and the feedback acoustic waves immediately outside the jet. Evidence will be presented to show that the screech frequency is largely controlled by the characteristics of the feedback acoustic waves. The feedback loop is driven by the instability wave of the jet. Thus the tone intensity and its occurrence are dictated by the characteristics of the instability wave. In this paper the dependence of the instability wave spectrum on the azimuthal mode number (axisymmetric or helical/flapping mode, etc.), the jet-to-ambient gas temperature ratio, and the jet Mach number are studied. The results of this study provide an explanation for the observed screech tone mode switch phenomenon (changing from axisymmetric to helical mode as Mach number increases) and the often-cited experimental observation that tone intensity reduces with increase in jet temperature. For ducted supersonic jets screech tones can also be generated by feedback loops formed by the coupling of normal duct modes to instability waves of the jet. The screech frequencies are dictated by the frequencies of the duct modes. Super resonance, resonance involving very large pressure oscillations, can occur when the feedback loop is powered by the most amplified instability wave. It is proposed that the observed large amplitude pressure fluctuations and tone in the test cells of Arnold Engineering Development Center were generated by super resonance. Estimated super-resonance frequency for a Mach 1.3 axisymmetric jet tested in the facility agrees well with measurement.
Tam, C. K. W.↗
Long-wave morphological instabilities in the directional solidification of a dilute binary mixture
Long-wave instabilities in a directionally-solidified binary mixture may occur in several limits. Sivashinsky (1983) identified a small-segregation-coefficient limit and obtained a weakly nonlinear evolution equation governing subcritical two-dimensional bifurcation. Brattkus and Davis (1988) identified a near-absolute-stability limit and obtained a strongly nonlinear evolution equation governing supercritical two-dimensional bifurcation. The present investigation identifies a third strongly nonlinear evolution equation, arising in the small-segregation-coefficient, large-surface-energy limit. This equation links both of the former and describes the change from the sub- to super-critical bifurcations. This study sets the previous long-wave analyses into a logical framework.
Riley, D. S.↗
Studies on Equatorial Shock Formation During Plasmaspheric Refilling
During the grant period from August 1, 1994 to October 31, 1995 we have continued to investigate the effects of plasma wave instabilities on the early stage plasmaspheric refilling. Since ion beams are the primary feature of the interhemispheric plasma flows during the early stage refilling, ion-beam driven instabilities and associated waves are of primary interest. The major findings of this research are briefly summarized here. After a systematic examination of the relevant plasma instabilities, we realized that when the interhemispheric plasma flows begin to interpenetrate at the equator, the most relevant plasma instability is the electrostatic ion cyclotron wave instability. Only at later stages the ion-acoustic instability may be affecting the plasma flow. An interesting property of the electrostatic ion cyclotron wave is that it heats ions perpendicular to the magnetic field. When the ions in the field-aligned flows are transversely heated, they are trapped in the magnetic flux tube, thus affecting the refilling process. The eic wave instability is a microprocess with scale length of the order of ion Larmor radius and the corresponding time scale is the ion cyclotron period. We have attempted to tackle the problem for the plasmaspheric refilling by incorporating the effects of eic wave instability on the mesoscale plasma flow when the properties of the latter exceeds the critical conditions for the former. We have compared the results on refilling from the model with and without the eic instability effects.
Singh, Nagendra↗
Transmitted sound field due to an impulsive line acoustic source bounded by a plate followed by a vortex sheet
The propagation of sound due to a line acoustic source in the moving stream across a semiinfinite vortex sheet which trails from a rigid plate is examined in a linear theory for the subsonic case. A solution for the transmitted sound field is obtained with the aid of multiple integral transforms and the Wiener-Hopf technique for both the steady state (time harmonic) and initial value (impulsive source) situations. The contour of inverse transform and hence the decomposition of the functions are determined through causality and radiation conditions. The solution obtained satisfies causality and the full Kutta conditions. The transmitted sound field is composed of two waves in both the stady state and initial value problems. One is the wave scattered from the edge of the plate which is associated with the bow wave and the instability wave. These waves exist in the downstream sectors. The other is the wave transmitted through the vortex sheet which is also associated with the instability wave. Regional divisions of the transmitted sound field are identified.
Miura, T.↗
Waves and instabilities in a magnetized plasma
Work on computer simulation of waves and instabilities in magnetized plasmas is reviewed. Included are verification of linear theory. Particular emphasis is given to investigation of nonlinear processes involved in the saturation of instabilities and of wave damping; these include a nonlinear cyclotron resonance and particle trapping in intense waves.
Dawson, J. M.↗
Comets - A laboratory for plasma waves and instabilities
The review discusses the various plasma waves and instabilities detected in the vicinity of comets. Particular emphasis is placed on nonlinear wave evolution, as well as the role of nonlinear waves in wave-particle interactions. Areas that need further research are identified to help persons who wish to contribute to the field.
Tsurutani, Bruce T.↗
Plasma waves and instabilities
An account is given of the waves and instabilities occurring at collisionless shocks, with attention to the mechanisms responsible for the generation of these waves. The transition region of the shock usually involves an abrupt broadband burst of electrostatic noise that extends from below the lower hybrid resonance to near the electron plasma frequency, and by a broadband burst of whistler mode EM noise below the electron cyclotron frequency. Electrostatic lower hybrid waves are also noted. Upstream of the shock, electron plasma oscillations, ion acoustic waves, and intense ULF MHD waves are often observed. The region downstream of the shock is usually very chaotic; electrostatic waves often extend long distances into the downstream region, together with whistler mode emissions.
Gurnett, Donald A.↗
Waves and instabilities
The U.S research activities during the mid-1982 to mid-1986 period in the area of plasma waves and instabilities are described. The principal results obtained by satellite observations and theoretical research can be divided into the following six categories: (1) whistler-mode wave-electron interactions, (2) wave-induced particle precipitation, (3) ULF wave phenomena, (4) ion-mode waves and instabilities, (5) auroral kilometric radiation, and (6) ionospheric irregularities and instabilities. In addition, waves and instabilities found in the outer magnetosphere, including the geomagnetic tail, magnetopause, and bow shock regions, are briefly discussed.
Inan, Umran S.↗
The noise from supersonic elliptic jets
This paper presents calculations of the noise radiated by a supersonic elliptic jet. The large scale structures in the jet, that are the predominant source of noise in the downstream direction, are modeled as instability waves. The evolution of the instability waves is determined by a local, linear, inviscid analysis. An expression is derived for the acoustic field outside the jet and the far field directivity associated with each instability wave. Calculations are performed for a Mach 1.5 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 2:1 and a Mach 2.0 elliptic jet with aspect ratio 3:1. The mean flow development is taken from experimental results. Comparisons are made with far field acoustic measurements.
Morris, Philip J.↗
Axial mode shock wave combustion instability in liquid propellant rocket engines
Axial mode shock wave combustion instability in liquid propellant rocket engines
SHOCK WAVE↗
Instability of rectangular jets
The instability of rectangular jets is investigated using a vortex-sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. It is demonstrated that the boundary element method can be used to calculate the dispersion relations and eigenfunctions of these instability wave modes. The method is robust and efficient. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.
Tam, Christopher K. W.↗
Noise from Supersonic Coaxial Jets: Inverted Velocity Profile - Part 3
The instability wave noise generation model is used to study the instability waves in the two shear layers of an inverted velocity profile, supersonic, coaxial jet and the noise radiated from the dominant wave. The inverted velocity profile jet has a high speed outer stream surrounding a low speed inner stream and the outer shear layer is always larger than the inner shear layer. The jet mean flows are calculated numerically. The operating conditions are chosen to exemplify the effect of the coaxial jet outer shear layer initial spreading rates. Calculations are made for the stability characteristics in the coaxial jet shear layers and the noise radiated from the instability waves for different operating conditions with the same total thrust, mass flow and exit area as a single reference jet. Results for inverted velocity profile jets indicate that relative maximum instability wave amplitudes and far field peak noise levels can be reduced from that of the reference jet by having higher spreading rates for the outer shear layer, low velocity ratios, and outer streams hotter than the inner stream.
Dahl, Milo D.↗
The prediction of noise radiation from supersonic elliptic jets
This paper describes the prediction of noise radiation from supersonic elliptic jets. The noise is associated with the large scale structures in the jet mixing layer. These structures are described as instability waves. The local characteristics of the instability waves are determined from a compressible, linear, analysis. The jet mean velocity and density are described in elliptic cylindrical coordinates. The local eigensolution for the instability waves is determined from a finite difference solution of the non-separable boundary value problem. This inner solution which is formulated in terms of the method of multiple scales is matched with the radiated field using the method of matched asymptotic expansions. The form of the far-field directivity is derived. Predictions are presented for the noise radiation by the several modes of instability in the elliptic jet. The radiated field is not axisymmetric and certain modes radiate strongly in the directions of the major and minor axes of the jet. The extension of the present work to other geometries and flow fields is discussed.
Morris, Philip J.↗
Instability of rectangular jets
The instability of rectangular jets is investigated using a vortex sheet model. It is shown that such jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their mode shapes or eigenfunctions is proposed. A parametric study of the instability wave characteristics has been carried out. A sample of the numerical results is reported here. It is found that the first and third modes of each instability wave family are corner modes. The pressure fluctuations associated with these instability waves are localized near the corners of the jet. The second mode, however, is a center mode with maximum fluctuations concentrated in the central portion of the jet flow. The center mode has the largest spatial growth rate. It is anticipated that as the instability waves propagate downstream the center mode would emerge as the dominant instability of the jet.
Tam, Christopher K. W.↗
Modern developments in shear flow control with swirl
Passive and active control of swirling turbulent jets is experimentally investigated. Initial swirl distribution is shown to dominate the free jet evolution in the passive mode. Vortex breakdown, a manifestation of high intensity swirl, was achieved at below critical swirl number (S = 0.48) by reducing the vortex core diameter. The response of a swirling turbulent jet to single frequency, plane wave acoustic excitation was shown to depend strongly on the swirl number, excitation Strouhal number, amplitude of the excitation wave, and core turbulence in a low speed cold jet. A 10 percent reduction of the mean centerline velocity at x/D = 9.0 (and a corresponding increase in the shear layer momentum thickness) was achieved by large amplitude internal plane wave acoustic excitation. Helical instability waves of negative azimuthal wave numbers exhibit larger amplification rates than the plane waves in swirling free jets, according to hydrodynamic stability theory. Consequently, an active swirling shear layer control is proposed to include the generation of helical instability waves of arbitrary helicity and the promotion of modal interaction, through multifrequency forcing.
Farokhi, Saeed↗