Shock wave structure by several new modeled Boltzmann equations
Shock wave structure prediction by nonlinear kinetic models with Monte Carlo solutions of full Boltzmann equation
Ferziger, J. H.↗
SEARCH · Engineering Papers
Results for “wave equation”
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Circular polarization of obliquely propagating whistler wave magnetic field
The circular polarization of the magnetic field of obliquely propagating whistler waves is derived using a basis set associated with the wave partial differential equation. The wave energy is mainly magnetic and the wave propagation consists of this magnetic energy sloshing back and forth between two orthogonal components of magnetic field in quadrature. The wave electric field energy is small compared to the magnetic field energy.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil
A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.
Hariharan, S. I.↗
Time domain numerical calculations of unsteady vortical flows about a flat plate airfoil
A time domain numerical scheme is developed to solve for the unsteady flow about a flat plate airfoil due to imposed upstream, small amplitude, transverse velocity perturbations. The governing equation for the resulting unsteady potential is a homogeneous, constant coefficient, convective wave equation. Accurate solution of the problem requires the development of approximate boundary conditions which correctly model the physics of the unsteady flow in the far field. A uniformly valid far field boundary condition is developed, and numerical results are presented using this condition. The stability of the scheme is discussed, and the stability restriction for the scheme is established as a function of the Mach number. Finally, comparisons are made with the frequency domain calculation by Scott and Atassi, and the relative strengths and weaknesses of each approach are assessed.
Hariharan, S. I.↗
Electronic optics in graphene in the semiclassical approximation
Highlights: • A rigorous semiclassical theory for the two-dimensional Dirac equation is developed. • We discuss how the use of eikonal coordinates greatly simplifies the theory. • Electronic optics in graphene is developed beyond the standard WKB approximation. • The semiclassical phase essentially affects electron focusing in graphene. - Abstract: We study above-barrier scattering of Dirac electrons by a smooth electrostatic potential combined with a coordinate-dependent mass in graphene. We assume that the potential and mass are sufficiently smooth, so that we can define a small dimensionless semiclassical parameter h≪1. This electronic optics setup naturally leads to focusing and the formation of caustics, which are singularities in the density of trajectories. We construct a semiclassical approximation for the wavefunction in all points, placing particular emphasis on the region near the caustic, where the maximum of the intensity lies. Because of the matrix character of the Dirac equation, this wavefunction contains a nontrivial semiclassical phase, which is absent for a scalar wave equation and which influences the focusing. We carefully discuss the three steps in our semiclassical approach: the adiabatic reduction of the matrix equation to aneffective scalar equation, the construction of the wavefunction using the Maslov canonical operator and the application of the uniform approximation to the integral expression for the wavefunction in the vicinity of a caustic. We consider several numerical examples and show that our semiclassical results are in very good agreement with the results of tight-binding calculations. In particular, we show that the semiclassical phase can have a pronounced effect on the position of the focus and its intensity.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
The heating of coronal loops by MHD waves
A detailed derivation of the MHD wave equation appropriate for solar coronal conditions is presented. Some general concepts are discussed regarding the propagation of MHD waves in regions where gradients in the Alfven speed exist. A solution of the ideal equation is discussed, and the ideal solution near the surface of the resonance layer is obtained. The dissipative solution is found and the matching between the ideal and dissipative solutions is demonstrated. The heating rate is calculated and the expression for the heating rate is used to estimate the wave amplitude which is necessary in the corona to explain the observed active region heating rate on the sun.
Davila, Joseph M.↗
Investigation to define the propagation characteristics of a finite amplitude acoustic pressure wave
A theoretical analysis of the propagation characteristics of a finite amplitude pressure wave is presented. The analysis attempts to study the contribution of entropy-producing regions to the mechanism of aerodynamic noise generation. It results in a nonlinear convective wave equation in terms of entropy and a thermodynamic 'J' function. A direct analogy between the derived governing equation and those used in classical literature is obtained. An idealization of the processes considered permits the uncoupling of the equations of motion with a consequent construction of an acoustic analogy treating shock wave emission of finite amplitude acoustic waves. An engineering approach is reflected in the concept of an extended plug nozzle whose function is to facilitate aerodynamic noise attenuation by modifying the entropy-producing regions.
Peter, A. C.↗
Some aspects of the identification of continuous vibrating systems
This paper deals with the identification of systems described by the one-dimensional, second order wave equation. Such equations arise commonly in various areas of mathematical physics, such as, acoustics, elastic wave propagation, and electromagnetic theory. Assuming that suitable measurements are made at only one point in the spatial domain, sufficient conditions for unique identification of the system eigenvalues and system coefficients are presented.
Udwadia, F. E.↗
Some Results Relevant to Statistical Closures for Compressible Turbulence
For weakly compressible turbulent fluctuations there exists a small parameter, the square of the fluctuating Mach number, that allows an investigation using a perturbative treatment. The consequences of such a perturbative analysis in three different subject areas are described: 1) initial conditions in direct numerical simulations, 2) an explanation for the oscillations seen in the compressible pressure in the direct numerical simulations of homogeneous shear, and 3) for turbulence closures accounting for the compressibility of velocity fluctuations. Initial conditions consistent with small turbulent Mach number asymptotics are constructed. The importance of consistent initial conditions in the direct numerical simulation of compressible turbulence is dramatically illustrated: spurious oscillations associated with inconsistent initial conditions are avoided, and the fluctuating dilatational field is some two orders of magnitude smaller for a compressible isotropic turbulence. For the isotropic decay it is shown that the choice of initial conditions can change the scaling law for the compressible dissipation. A two-time expansion of the Navier-Stokes equations is used to distinguish compressible acoustic and compressible advective modes. A simple conceptual model for weakly compressible turbulence - a forced linear oscillator is described. It is shown that the evolution equations for the compressible portions of turbulence can be understood as a forced wave equation with refraction. Acoustic modes of the flow can be amplified by refraction and are able to manifest themselves in large fluctuations of the compressible pressure.
Ristorcelli, J. R.↗
Non-linear Least Square Fitting Technique for the Determination of Field Line Resonance Frequency in Ground Magnetometer Data: Application to Remote Sensing of Plasmaspheric Mass Density
The accurate determination of the Field Line Resonance (FLR) frequency of a resonating geomagnetic field line is necessary to remotely monitor the plasmaspheric mass density during geomagnetic storms and quiet times alike. Under certain assumptions the plasmaspheric mass density at the equator is inversely proportional to the square of the FLR frequency. The most common techniques to determine the FLR frequency from ground magnetometer measurements are the amplitude ratio and phase difference techniques, both based on geomagnetic field observations at two latitudinally separated ground stations along the same magnetic meridian. Previously developed automated techniques have used statistical methods to pinpoint the FLR frequency using the amplitude ratio and phase difference calculations. We now introduce a physics-based automated technique, using non-linear least square fitting of the ground magnetometer data to the analytical resonant wave equations, that reproduces the wave characteristics on the ground, and from those determine the FLR frequency. One of the advantages of the new technique is the estimation of physics-based errors of the FLR frequency, and as a result of the equatorial plasmaspheric mass density. We present analytical results of the new technique, and test it using data from the Inner-Magnetospheric Array for Geospace Science (iMAGS) ground magnetometer chain along the coast of Chile and the east coast of the United States. We compare the results with the results of previously published statistical automated techniques.
A. Boudouridis↗
Shear wave generation by mode conversion in picosecond ultrasonics: Impact of grain orientation and material properties
Abstract Picosecond ultrasonics has seen wide application in the investigation of interfaces in semiconductors and 3D imaging in biological systems. Shear ultrasonic waves are important for elastic constant and grain orientation measurement in ceramic materials. In this study, we investigate the impact of grain orientation and material's elastic properties on the generation efficiency of shear waves by mode conversion at a transducer thin film/substrate interface. The solution of acoustic wave equations suggests that crystal grain orientation has a strong impact on the generated shear wave amplitude. This dependence is found to be closely related to the magnitude of longitudinal component of wave displacements. The applicability of analytical model is validated by the experimental results from time‐domain Brillouin scattering. Moreover, material properties determine acoustic wave amplitudes based on the acoustic mismatch model and, particularly, large elastic anisotropy defined by Zener ratio favors strong shear waves. In the light of this analysis, several recommendations on suitable grain orientations and film materials are made to facilitate shear wave detection.
Wang, Yuzhou↗
Nonlinear stress waves in a perfectly flexible string
This paper discusses nonlinear stress-wave propagation in a perfectly flexible string obeying a quasilinear (rate-dependent) constitutive equation. Wave speeds and compatibility relations valid along various families of characteristics were determined. It was shown that the compatibility relations associated with the transverse as well as the longitudinal waves readily yield a physical interpretation when they are expressed in suitable variables and in vector form. Coding based on the present information was completed for the machine solution of a class of mixed initial- and boundary-value problems of practical interest. Computer simulation of the stress-wave interaction in the 40-foot lanyard in the Arcas 'Rocoz' system during deployment was carried out using a stress-strain relation for nylon at the strain rate of 30/second. A method for estimating the maximum tension and strain in a string during the initial loading phase is proposed.
Fan, D.-N.↗
Slow Wave Vane Structure with Elliptical Cross-Section Slots, an Analysis
Mathematical analysis of the wave equation in cylinders with elliptical cross-section slots was performed. Compared to slow wave structures with rectangular slots higher impedance and lower power dissipation losses are evident. These features could lead to improved designs of traveling wave magnetrons and gigahertz backward-wave oscillators as well as linear traveling wave tubes with relatively shallow slots.
Kosmahl, Henry G.↗
Non-Reflecting Regions for Finite Difference Methods in Modeling of Elastic Wave Propagation in Plates
Solution of the wave equation using techniques such as finite difference or finite element methods can model elastic wave propagation in solids. This requires mapping the physical geometry into a computational domain whose size is governed by the size of the physical domain of interest and by the required resolution. This computational domain, in turn, dictates the computer memory requirements as well as the calculation time. Quite often, the physical region of interest is only a part of the whole physical body, and does not necessarily include all the physical boundaries. Reduction of the calculation domain requires positioning an artificial boundary or region where a physical boundary does not exist. It is important however that such a boundary, or region, will not affect the internal domain, i.e., it should not cause reflections that propagate back into the material. This paper concentrates on the issue of constructing such a boundary region.
Kishoni, Doron↗
Propagation of a finite-amplitude elastic pulse in a bar of Berea sandstone: A detailed look at the mechanisms of classical nonlinearity, hysteresis, and nonequilibrium dynamics: Nonlinear propagation of elastic pulse
Here, we study the propagation of a finite-amplitude elastic pulse in a long thin bar of Berea sandstone. In previous work, this type of experiment has been conducted to quantify classical nonlinearity, based on the amplitude growth of the second harmonic as a function of propagation distance. To greatly expand on that early work, a non-contact scanning 3D laser Doppler vibrometer was used to track the evolution of the axial component of the particle velocity over the entire surface of the bar as functions of the propagation distance and source amplitude. With these new measurements, the combined effects of classical nonlinearity, hysteresis, and nonequilibrium dynamics have all been measured simultaneously. We then show that the numerical resolution of the 1D wave equation with terms for classical nonlinearity and attenuation accurately captures the spectral features of the waves up to the second harmonic. But, for higher harmonics the spectral content is shown to be strongly influenced by hysteresis. This work also shows data which not only quantifies classical nonlinearity but also the nonequilibrium dynamics based on the relative change in the arrival time of the elastic pulse as a function of strain and distance from the source. Finally, a comparison is made to a resonant bar measurement, a reference experiment used to quantify nonequilibrium dynamics, based on the relative shift of the resonance frequencies as a function of the maximum dynamic strain in the sample.
58 GEOSCIENCES↗
Far field effects of weak spatially periodic inhomogeneities.
Small variations in the properties of an acoustic medium produce cumulative effects that significantly alter wave forms propagating over long distances. To investigate some aspects of these effects, without statistical models, the one-dimensional wave equation with a weak spatially periodic variation in the sound speed is treated. An approximation is developed valid for such weak inhomogeneities over large distances based upon the approximate treatment of a linear differential equation with a periodic coefficient. It is applied to the propagation of an initial step wave and identifies the dispersive nature of the medium which accounts for the cumulative effects.
Friedman, M. B.↗
A Computing Method for Sound Propagation Through a Nonuniform Jet Stream
Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.
Padula, S. L.↗
A computing method for sound propagation through a nonuniform jet stream
The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.
Padula, S. L.↗