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Theory of temperature dependent magnon energies in antiferromagnets based on spin wave operator expansion of Hamiltonian, taking into account dynamical interaction between waves
An overview of parabolic and PNS (Parabolized Navier-Stokes) methodology developed to treat highly curved sub and supersonic wall jets is presented. The fundamental data base to which these models were applied is discussed in detail. The analysis of strong curvature effects was found to require a semi-elliptic extension of the parabolic modeling to account for turbulent contributions to the normal pressure variations, as well as an extension to the turbulence models utilized, to account for the highly enhanced mixing rates observed in situations with large convex curvature. A noniterative, pressure split procedure is shown to extend parabolic models to account for such normal pressure variations in an efficient manner, requiring minimal additional run time over a standard parabolic approach. A new PNS methodology is presented to solve this problem which extends parabolic methodology via the addition of a characteristic base wave solver. Applications of this approach to analyze the interaction of wave and turbulence processes in wall jets is presented.
In this paper, a model is developed for the analysis of the electrostatic waves produced in the shock foot at Jupiter. It is shown that an ion beam instability involving the ions reflected at the shock ramp and the incoming solar-wind electrons produces waves at the observed frequencies and that saturation via orbit diffusion limits the waves to amplitudes near to what is observed. Results from a two-dimensional model of the reflected beam in the foot indicate that the waves propagate against the solar wind away from the shock ramp and are amplified up to their saturation amplitudes. The saturation results, combined with the electron temperature profile due to wave-particle interactions predicted by quasi-linear theory, reproduce a wave amplitude profile for the shock foot that is in reasonable agreement with the observations.
We describe initial results from a time-dependent, semi-kinetic model of plasma outflow incorporating wave-particle interactions along current-carrying auroral field lines. Electrostatic waves are generated by the current driven ion cyclotron instability (CDICI), causing perpendicular velocity diffusion of ions plus electron heating via anomalous resistivity when and where the relative drift between electrons and ions exceeds certain critical velocities. Using the local bulk parameters we calculate these critical velocities, and so are able to self-consistently switch on and off the heating of the various particle species. Due to the dependence of these critical velocities on the bulk parameters of the species the heating effects exhibit quite complex spatial and temporal variations. A wide range of ion distribution functions are observed in these simulations, including conics with energies of a few electron volts and 'ring' distributions. The rings are seen to be a natural result of transverse heating and velocity filter effects and do not require coherent acceleration processes. We also observe the formation of a density depletion in hydrogen and enhanced oxygen densities at high altitudes.
Uniform high order spectral methods to solve multi-dimensional Euler equations for gas dynamics are discussed. Uniform high order spectral approximations with spectral accuracy in smooth regions of solutions are constructed by introducing the idea of the Essentially Non-Oscillatory (ENO) polynomial interpolations into the spectral methods. The authors present numerical results for the inviscid Burgers' equation, and for the one-dimensional Euler equations including the interactions between a shock wave and density disturbance, Sod's and Lax's shock tube problems, and the blast wave problem. The interaction between a Mach 3 two-dimensional shock wave and a rotating vortex is simulated.
It is argued that the formulation used by Gombosi (1991) does not distinguish between two fundamental types of resonant interactions (those between cometary pickup ions and LF electromagnetic waves). Two problems arise from using their overly simplified expressions. The wave polarization of the solar wind Alfven wave is not purely right-handed, and values from alpha sub com and alpha sub sw are not well known, nor are the 'polarizations' of the 'backward'-going waves in either case. Gombosi et al. discuss the antisunward vs the sunward propagating solar wind Alfven wave, and assume a reasonable value of 0.2 for alpha sub sw. However, alpha sub com is totally unknown. It is concluded that a more correct analysis of wave polarization can lead to significant changes in the formulation and results from Gombosi et al. In his reply Gombosi argues that his simplified wave-particle interaction model is consistent with Giotto observations and plasma kinetic simulations and it leads to a reasonable approximation of the implanted ion transport coefficients. The more complicated approach suggested by Tsurutani & Thorne (1993) requires the introduction of several ad hoc parameters and it does not lead to any change of the energy diffusion coefficient.
Whistler mode chorus waves are particularly important in outer radiation belt dynamics due to their key role in controlling the acceleration and scattering of electrons over a very wide energy range. The key parameters for both nonlinear and quasi-linear treatment of wave-particle interactions are the temporal and spatial scales of the wave source region and coherence of the wave field perturbations. Neither the source scale nor the coherence scale is well established experimentally, mostly because of a lack of multipoint VLF waveform measurements. We present an unprecedentedly long interval of coordinated VLF waveform measurements (sampled at 16384 s(exp -1)) aboard the two Van Allen Probes spacecraft-9 h (0800-1200 UT and 1700-2200 UT) during two consecutive apogees on 15 July 2014. The spacecraft separations varied from about 100 to 5000 km (mostly radially); measurements covered an L shell range from 3 to 6; magnetic local time 0430-0900, and magnetic latitudes were approximately 15 and approximately 5 deg during the two orbits. Using time-domain correlation techniques, the single chorus source spatial extent transverse to the background magnetic field has been determined to be about 550-650 km for upper band chorus waves with amplitudes less than 100 pT and up to 800 km for larger amplitude, lower band chorus waves. The ratio between wave amplitudes measured on the two spacecraft is also examined to reveal that the wave amplitude distribution within a single chorus element generation area can be well approximated by a Gaussian exp(-0.5 x r (exp 2)/r(sub 0)(exp 2)), with the characteristic scale r(sub 0) around 300 km. Waves detected by the two spacecraft were found to be coherent in phase at distances up to 400 km.
Presented is an application of wave potential formulation (WPF) together with domain reduction method (DRM) to modeling earthquake soil structure interaction (ESSI) behavior in horizontally layered ground under inclined incident seismic waves. Wave potential formulation is used to develop a spatially varying, inclined seismic wave field from incident Primary (P) and Secondary (S) waves that propagate through layered ground. Developed seismic wave field is then used to develop effective forces for Domain Reduction Method that are then used for analyzing ESSI response of a soil structure system. Developed methodology, called WPF-DRM, is verified using analytic solution for a free field response of layered ground subjected to inclined incident waves. Developed WPF-DRM methodology is illustrated through analysis of an ESSI response of a deeply embedded structure, a small modular reactor (SMR) subjected to incident S wave polarized in vertical plane (SV) with variation in inclinations and frequencies. Presented example highlights the influences of incident wave inclination and frequency on ESSI response of analyzed SMR.
An asymptotic description is derived for the interaction between a shock wave and a turbulent boundary layer in transonic flow, for a particular limiting case. The dimensionless difference between the external flow velocity and critical sound speed is taken to be much smaller than one, but large in comparison with the dimensionless friction velocity. The basic results are derived for a flat plate, and corrections for longitudinal wall curvature and for flow in a circular pipe are also shown. Solutions are given for the wall pressure distribution and the shape of the shock wave. Solutions for the wall shear stress are obtained, and a criterion for incipient separation is derived. Simplified solutions for both the wall pressure and skin friction distributions in the interaction region are given. These results are presented in a form suitable for use in computer programs.
We review comprehensive observations of electromagnetic ion cyclotron (EMIC) wave-driven energetic electron precipitation using data collected by the energetic electron detector on the Electron Losses and Fields InvestigatioN (ELFIN) mission, two polar-orbiting low-altitude spinning CubeSats, measuring 50-5000 keV electrons with good pitch-angle and energy resolution. EMIC wave-driven precipitation exhibits a distinct signature in energy-spectrograms of the precipitating-to-trapped flux ratio: peaks at >0.5 MeV which are abrupt (bursty) (lasting ~17 s, or ΔL ~ 0.56) with significant substructure (occasionally down to sub-second timescale). We attribute the bursty nature of the precipitation to the spatial extent and structuredness of the wave field at the equator. Multiple ELFIN passes over the same MLT sector allow us to study the spatial and temporal evolution of the EMIC wave - electron interaction region. Case studies employing conjugate ground-based or equatorial observations of the EMIC waves reveal that the energy of moderate and strong precipitation at ELFIN approximately agrees with theoretical expectations for cyclotron resonant interactions in a cold plasma. Using multiple years of ELFIN data uniformly distributed in local time, we assemble a statistical database of ~50 events of strong EMIC wave-driven precipitation. Most reside at L ~ 5 – 7 at dusk, while a smaller subset exists at L ~ 8 – 12 at post-midnight. The energies of the peak-precipitation ratio and of the half-peak precipitation ratio (our proxy for the minimum resonance energy) exhibit an L-shell dependence in good agreement with theoretical estimates based on prior statistical observations of EMIC wave power spectra. The precipitation ratio’s spectral shape for the most intense events has an exponential falloff away from the peak (i.e., on either side of ~ 1.45 MeV). It too agrees well with quasi-linear diffusion theory based on prior statistics of wave spectra. It should be noted though that this diffusive treatment likely includes effects from nonlinear resonant interactions (especially at high energies) and nonresonant effects from sharp wave packet edges (at low energies). Sub-MeV electron precipitation observed concurrently with strong EMIC wave-driven >1 MeV precipitation has a spectral shape that is consistent with efficient pitch-angle scattering down to ~ 200-300 keV by much less intense higher frequency EMIC waves at dusk (where such waves are most frequent). At ~100 keV, whistler-mode chorus may be implicated in concurrent precipitation. These results confirm the critical role of EMIC waves in driving relativistic electron losses. Nonlinear effects may abound and require further investigation.
While electromagnetic ion cyclotron (EMIC) waves have been long studied as a scattering mechanism for ultrarelativistic (megaelectron volt) electrons via cyclotron‐resonant interactions, these waves are also of the right frequency to resonate with the bounce motion of lower‐energy (approximately tens to hundreds of kiloelectron volts) electrons. Here we investigate the effectiveness of this bounce resonance interaction to better determine the effects of EMIC waves on subrelativistic electron populations in Earth's inner magnetosphere. Using wave and plasma parameters directly measured by the Van Allen Probes, we estimate bounce resonance diffusion coefficients for four different events, illustrative of wave and plasma parameters to be encountered in the inner magnetosphere. The range of electron energies and pitch angles affected is examined to better assess the realistic effects of EMIC‐driven bounce resonance on energetic electron populations based on actual, locally observed event‐based parameters. Significant local diffusion coefficients (~ > 10(exp −6) s(exp −1)) for 50‐ to 100‐keV electrons are achieved for both H+ band wave events as well as He+ band, with diffusion coefficients peaking for near‐90° pitch angles but remaining elevated for intermediate ones as well. Diffusion coefficients for higher‐energy 200‐keV electrons are typically multiple orders of magnitude lower (ranging from 10(exp −11) to 10(exp −6) s(exp −1)) and often peak at lower pitch angles (~20–30°). These results suggest that both H+ and He+ band EMIC waves can play a role in shaping lower‐energy electron dynamics via bounce‐resonant interactions, in addition to their role in relativistic electron loss via cyclotron resonance.
A three-dimensional, severely truncated, quasi-geostrophic model in a beta channel is used to explore the dynamics of the observed anticorrelation between the amplitudes of planetary waves 1 and 2 in the Northern Hemisphere winter stratosphere. The model, which includes interactions among eight horizontal modes, generates realistic wave 1-wave 2 vacillations when westward traveling wave 1 interacts with stationary waves 1 and 2. It is found that while wave 1 oscillates in response to wave-mean flow interactions, the oscillations in the amplitude of wave 2 are driven primarily by wave-wave interactions. Experiments with a barotropic model reveal that the timing of the strongest wave-wave interactions is determined by the wave 1 interaction with the mean flow.
Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.
Direct numerical simulation is used to evaluate a weakly nonlinear theory describing the interaction of Tollmien-Schlichting waves with Dean vortices in curved channel flow. The theory and the simulation agree for certain combinations of parameters, but the two approaches give conflicting results for other combinations. Some possibilities for these discrepancies are discussed.
The experimental key to observing stochasticity or turbulence in a distribution of interacting propagating waves is the achievement of high amplitude and the use of a medium with a large coefficient of nonlinearity. The research indicates that capillary waves are the best means of observing this phenomenon; however, gravitational modifications of the capillary wave dispersion law greatly reduce the large coefficient of nonlinearity. Thus, a search for wave turbulence in a large drop of fluid that is positioned in a microgravity experiment was conducted. Capillary waves that run around the surface of the drop are excited, and their power spectrum and higher order correlations are analyzed for wave turbulence. The theoretical calculations indicate that modulations of the power spectrum should propagate as second sound waves. These issues have consequences for signal processing and plasma confinement.
Fluctuating wall-pressure measurements are made in shock-wave/turbulent-boundary-layer interactions generated by sharp/unswept fins at angles of attack of 16, 18, 20, 22, 24, 26, and 28 degrees at Mach 5. The experiment was conducted under approximately adiabatic wall temperature conditions. The mean and rms pressure distributions can be collapsed in conical coordinates. The wall-pressure signal near separation is intermittent for all angles of attack (16-28 deg) and is qualitatively similar to that measured in unswept flows. However, the shock frequencies are higher - about 5 kHz compared to 0.5-1 kHz. Over the range of sweepbacks examined, from 25-55 deg, the spectral content of the fluctuating pressures does not change. Thus, the increase in separation-shock frequency from 1 to 5 kHz occurs at lower interaction sweepback and is not a continuous process with increasing sweepback. Power spectra at the position of maximum rms in the intermittent region for interactions in different incoming boundary layers have the same center frequency. The maximum rms in the intermittent region correlates with interaction sweepback, not with overall inviscid pressure rise.
Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.
Shock wave–bubble interactions in water manifest rich dynamics driven by a combination of strong pressure and density mismatches. They have a wide variety of applications, including the injection of pharmaceuticals, and through scaling, enable the exploration of various aspects of high-energy-density systems such as inertial confinement fusion. In this work, the interaction between a micrometric nitrogen bubble and a planar shock wave, characterized by a Mach number of M = 1.24 and a peak pressure of p max = 0.57 , is experimentally recorded using ultra-high-speed x-ray phase contrast imaging. Highly resolved radiographs provide access to all phase discontinuities along the beam path, offering quantities such as the time-varying bubble size, the speed of a jet produced during the bubble collapse, and the time evolution of the shock wave front, which are critical benchmark data for numerical scheme validation. This study addresses the lack of well-characterized, repeatable, and high spatiotemporal resolution experiments at negative Atwood numbers by providing shock–bubble visualization and corresponding numerical simulation.