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Modifications to the existing inviscid theory of long-wave propagation in rotating fluids are studied. A modification to the Korteweg-deVries equation is found to describe weak dissipation in long waves in a swirling fluid. General features of solutions are discussed, and a solution for the damping of solitary waves is presented.
In a weakly inhomogeneous plasma, the large-amplitude Alfven waves propagating parallel to the ambient magnetic field are shown to evolve into accelerated Alfven solitons. Nonlinear interaction of the accelerated Alfven solitons with the Langmuir waves results in the emission of coherent radiations. Analytical expression for the power radiated per unit solid angle from a soliton is derived for two inhomogeneity profiles, namely the linear profile and the parabolic profile. For the case of uniform plasmas, the emission occurs via a decay-type process or resonant modes. In the presence of inhomogeneity, nonresonant modes provide a new channel for the emission of radiation. The power radiated per unit solid angle is computed for the parameters relevant to Comet Halley's plasma environment. For the nonresonant modes it is found to be several orders of magnitude higher than that for the case of resonant modes.
The linearized equations describing the propagation of sound in variable area ducts containing flow are shown to be singular when the duct mean flow is sonic. The singularity is removed when previously ignored nonlinear terms are retained. The results of a numerical study, for the case of plane waves propagating in a one-dimensional converging-diverging duct, show that the sound field is adequately described by the linearized equations only when the axial mean flow Mach number at the duct throat M sub th 0.6. For M sub th 0.6, the numerical results showed that acoustic energy flux was not conserved. An attempt was made to extend the study to include the nonlinear behavior of the sound field. Meaningful results were not obtained due, primarily, to numerical difficulties.
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; results of the standard linear theory are compared with the nonlinear results to assess the significance of the nonlinear terms. The nonlinear analysis represents the acoustic disturbance as a sum of interacting harmonics. Numerical results show that the basic signal is unaffected by the presence of higher harmonics if the throat Mach number is not too large, but as the Mach number approaches unity more harmonics are needed to describe the acoustic propagation. The strong interactions among harmonics in the numerical results occur in a region which is generally consistent with the nonlinear inner-expansion region of Callegari and Myers.
Internal gravity waves are one of the important phenomena in understanding the general circulation as well as eddy motions in the atmosphere, particularly in the mesosphere and lower thermosphere. Therefore, in order to reproduce the middle atmospheric general circulation, it is necessary to incorporate vertically propagating internal gravity waves into general circulation models (GCMs). Results from numerical simulations on nonlinear interactions between mean flow and internal gravity waves are briefly presented.
A consequence of an exoatmospheric nuclear burst is an electromagnetic pulse (EMP) radiated from it. In a region far enough away from the burst, where nonlinear effects can be ignored, the EMP can be represented by a large-amplitude narrow-time-width plane-wave pulse. If the ionosphere intervenes the origin and destination of the EMP, frequency dispersion can cause significant changes in the original pulse upon reception. A method of computing these dispersive effects of transient wave propagation is summarized. The method described is different from the standard transform techniques and provides physical insight into the transient wave process. The method, although exact, can be used in approximating the early-time transient response of an ionospheric region by a simple integration with only explicit knowledge of the electron density, electron collision frequency, and electron gyrofrequency required. As an illustration of the method, it is applied to a simple example and contrasted with the corresponding transform solution.
In recent Ultraviolet Coronagraph Spectrometer/Solar and Heliospheric Observatory (UVCS/SOHO) White Light Channel (WLC) observations we found quasi-periodic variations in the polarized brightness (pB) in the polar coronal holes at heliocentric distances of 1.9-2.45 solar radii. The motivation for the observation is the 2.5D Magnetohydrodynamics (MHD) model of solar wind acceleration by nonlinear waves, that predicts compressive fluctuations in coronal holes. To help identify the waves observed with the UVCS/WLC we model the propagation and dissipation of slow magnetosonic waves in polar plumes using 1D MHD code in spherical geometry, We find that the slow waves nonlinearly steepen in the gravitationally stratified plumes. The nonlinear steepening of the waves leads to enhanced dissipation due to compressive viscosity at the wave-fronts.
An investigation is conducted of five relativistic plane nonlinear waves, taking into account circularly polarized waves and electrostatic plasma oscillations propagating parallel to the magnetic field, relativistic Alfven waves, linearly polarized transverse waves propagating in zero magnetic field, and the relativistic analog of the extraordinary mode propagating at an arbitrary angle to the magnetic field. It is found that a large-amplitude superluminous wave determines the average plasma properties, and not vice versa. Attention is given to the implications of the obtained results for the acceleration of cosmic rays in pulsar magnetospheres.
A two dimensional two-fluid MHD model including anomalous resistivity was used to investigate the dynamics of magnetosphere-ionosphere coupling. When a field-aligned current is generated on auroral field lines, the disturbance propagates towards the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. Turbulence leads to absorption and reflection of the Alfven wave, partially decoupling the generator from the ionosphere. The approach to a steady-state is strongly dependent on the presence or absence of the turbulence. The current is self-limiting, since a current in excess of critical causes a diffusion of the magnetic field perturbation and a reduction of current.
The dynamics of magnetosphere-ionosphere coupling has been investigated by means of a two-dimensional two-fluid MHD model including anomalous resistivity. When field-aligned current is generated on auroral field lines, the disturbance propagates toward the ionosphere in the form of a kinetic Alfven wave. When the current exceeds a critical value, microscopic turbulence is produced, which modifies the propagation of the Alfven wave. This process is modeled by a nonlinear collision frequency, which increases with the excess of the drift velocity over the critical value. The system evolves toward an electrostatic structure, with the perpendicular electric field having a shorter scale than the field-aligned current. The approach to a steady state is strongly dependent on the presence or absence of the turbulence and on the boundary conditions imposed in the generator. As current is increased or scale size is decreased, the turbulent region reflects and absorbs most of the Alfven wave energy, decoupling the generator from the ionosphere.
This paper describes the experimental setup and measurement techniques used to investigate currents between tethered electodes in a magnetized laboratory plasma. Experimental results include information on current propagation, the formation of wave wings, the limits of current collection, nonlinear effects and instabilities, charging phenomena, and the characteristics of transmission lines in plasma. The results were found to support certain predictions on tethers in space (e.g., the MHD far zone or the motional emf) while contradicting others (e.g., distant current closure), and revealed such new phenomena as current disruptions, current-neutralized beams, and wing spread.
We study the propagation of waves across fixed mesh refinement boundaries in linear and nonlinear model equations in 1-D and 2-D, and in the 3-D Einstein equations of general relativity. We demonstrate that using linear interpolation to set the data in guard cells leads to the production of reflected waves at the refinement boundaries. Implementing quadratic interpolation to fill the guard cells eliminates these spurious signals.
Dislocation dipole substructures formed during metal fatigue are shown to produce a substantial distortion of ultrasonic waves propagating through the fatigued material. A model of ultrasonic wave-dislocation dipole interactions is developed that quantifies the wave distortion by means of a material nonlinearity parameter (beta). Application of the model to AA2024-T4 predicts a value of p approximately 300% larger in material cyclically loaded for 100 kcycles in stress-control at 276 MPa and R=0 than that measured for virgin material. Experimental measurements show a monotonic increase in p as a function of the number of fatigue cycles that closely approaches the predicted increase. The experiments also suggest that the relevant dislocation substructures are localized in the material.
The problem of the exitation of obliquely propagating magnetosonic waves which can steepen up (also known as shocklets) is considered. Shocklets have been observed upstream of the Earth's bow shock and at comets Giacobini-Zinner and Grigg-Skjellerup. Linear theory as well as two-dimensional (2-D) hybrid (fluid electrons, particle ions) simulations are used to determine the properties of waves generated by ring-beam velocity distributions in great detail. The effects of both proton and oxygen ring-beams are considered. The study of instabilities excited by a proton ring-beam is relevant to the region upstream of the Earth's bow shock, whereas the oxygen ring-beam corresponds to cometary ions picked up by the solar wind. Linear theory has shown that for a ring-beam, four instabilities are found, one on the nonresonant mode, one on the Alfven mode, and two along the magnetosonic/whistler branch. The relative growth rate of these instabilities is a sensitive function of parameters. Although one of the magnetosonic instabilities has maximum growth along the magnetic field, the other has maximum growth in oblique directions. We have studied the competition of these instabilities in the nonlinear regime using 2-D simulations. As in the linear limit, the nonlinear results are a function of beam density and distribution function. By performing the simulations as both initial value and driven systems, we have found that the outcome of the simulations can vary, suggesting that the latter type simulations is needed to address the observations. A general conclusion of the simulation results is that field-aligned beams do not result in the formation of shocklets, whereas ring-beam distributions can.
The complex region of Jupiter's radio emissions at decameter wavelengths, the so-called DAM, is considered, taking into account the basic theoretical ideas which underly both the older and newer theories and models. Linear theories are examined, giving attention to direct emission mechanisms, parallel propagation, perpendicular propagation, and indirect emission mechanisms. An investigation of nonlinear theories is also conducted. Three-wave interactions are discussed along with decay instabilities, and three-wave up-conversio. Aspects of the Io and plasma torus interaction are studied, and a mechanism by which Io can accelerate electrons is reviewed.
Exact solution of nonlinear relativistic equations of motion for electron in right circularly polarized wave propagating in whistler mode parallel to external magnetic field
Recent measurements from the plasma wave instrument on the Galileo spacecraft have shown that Langmuir waves observed in conjunction with a type III solar radio burst contain many beat-type waveforms, with beat frequencies ranging from about 150 to 650 Hz. Strong evidence exists that the beat pattern is produced by two closely spaced narrowband components. The most likely candidates for these two waves are a beam-generated Langmuir wave and an oppositely propagating Langmuir wave produced by parametric decay. In the parametric decay process, nonlinear interactions cause the beam-driven Langmuir wave to decay into a Langmuir wave and a low-frequency ion sound wave. Comparisons of the observed beat frequency are in good agreement with theoretical predictions for a three-wave parametric decay process. Weak low-frequency emissions are also sometimes observed at the predicted frequency of the ion sound wave.
Since their discovery over 100 years ago, there have been many suggestions for the origin and development of solar spicules. Because the velocities of spicules are comparable to the sound and Alfven speeds of the low chromosphere, linear theory cannot fully describe them. Consequently, detailed tests of theoretical ideas had to await the development of computing power that only became available during the 1970s. This work reviews theories for spicules and spicule-like features over approximately the past 25 years, with an emphasis on the models based on nonlinear numerical simulations. These models have given us physical insight into wave propagation in the solar atmosphere, and have helped elucidate how such waves, and associated shock waves, may be capable of creating motions and structures on magnetic flux tubes in the lower solar atmosphere. So far, however, it has been difficult to reproduce the most- commonly -quoted parameters for spicules with these models, using what appears to be the most suitable input parameters. A key impediment to developing satisfactory models has been the lack of reliable observational information, which is a consequence of the small angular size and transient lifetime of spicules. I close with a list of key observational questions to be addressed with space-based satellites, such as the currently operating TRACE satellite, and especially the upcoming Solar-B mission. Answers to these questions will help determine which, if any, of the current models correctly explains spicules.