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At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

FREQUENCY SHIFTS OF RESONANT MODES OF THE SUN DUE TO NEAR-SURFACE CONVECTIVE SCATTERING

Measurements of oscillation frequencies of the Sun and stars can provide important independent constraints on their internal structure and dynamics. Seismic models of these oscillations are used to connect structure and rotation of the star to its resonant frequencies, which are then compared with observations, the goal being that of minimizing the difference between the two. Even in the case of the Sun, for which structure models are highly tuned, observed frequencies show systematic deviations from modeled frequencies, a phenomenon referred to as the “surface term.” The dominant source of this systematic effect is thought to be vigorous near-surface convection, which is not well accounted for in both stellar modeling and mode-oscillation physics. Here we bring to bear the method of homogenization, applicable in the asymptotic limit of large wavelengths (in comparison to the correlation scale of convection), to characterize the effect of small-scale surface convection on resonant-mode frequencies in the Sun. We show that the full oscillation equations, in the presence of temporally stationary three-dimensional (3D) flows, can be reduced to an effective “quiet-Sun” wave equation with altered sound speed, Brünt–Väisäla frequency, and Lamb frequency. We derive the modified equation and relations for the appropriate averaging of 3D flows and thermal quantities to obtain the properties of this effective medium. Using flows obtained from 3D numerical simulations of near-surface convection, we quantify their effect on solar oscillation frequencies and find that they are shifted systematically and substantially. We argue therefore that consistent interpretations of resonant frequencies must include modifications to the wave equation that effectively capture the impact of vigorous hydrodynamic convection.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Progress in modeling atmospheric propagation of sonic booms

The improved simulation of sonic boom propagation through the real atmosphere requires greater understanding of how the transient acoustic pulses popularly termed sonic booms are affected by humidity and turbulence. A realistic atmosphere is invariably somewhat turbulent, and may be characterized by an ambient fluid velocity v and sound speed c that vary from point to point. The absolute humidity will also vary from point to point, although possibly not as irregularly. What is ideally desired is a relatively simple scheme for predicting the probable spreads in key sonic boom signature parameters. Such parameters could be peak amplitudes, rise times, or gross quantities obtainable by signal processing that correlate well with annoyance or damage potential. The practical desire for the prediction scheme is that it require a relatively small amount of knowledge, possibly of a statistical nature, concerning the atmosphere along, the propagation path from the aircraft to the ground. The impact of such a scheme, if developed, implemented, and verified, would be that it would give the persons who make planning decisions a tool for assessing the magnitude of environmental problems that might result from any given overflight or sequence of overflights. The technical approach that has been followed by the author and some of his colleagues is to formulate a hierarchy of simple approximate models based on fundamental physical principles and then to test these models against existing data. For propagation of sonic booms and of other types of acoustic pulses in nonturbulent model atmospheres, there exists a basic overall theoretical model that has evolved as an outgrowth of geometrical acoustics. This theoretical model depicts the sound as propagating within ray tubes in a manner analogous to sound in a waveguide of slowly varying cross-section. Propagation along the ray tube is quasi-one-dimensional, and a wave equation for unidirectional wave propagation is used. A nonlinear term is added to this equation to account for nonlinear steepening, and the formulation has been carried through to allow for spatially varying sound speed, ambient density, and ambient wind velocities. The model intrinsically neglects diffraction, so it cannot take into account what has previously been mentioned in the literature as possibly important mechanisms for turbulence-related distortion. The model as originally developed could predict an idealized N-waveform which often agrees with data in terms of peak amplitude and overall positive phase duration. It is possible, moreover, to develop simple methods based on the physics of relaxation processes for incorporating molecular relaxation into the quasi-one-dimensional model of nonlinear propagation along ray tubes.

Pierce, Allan D.↗
NASA NTRS1979

The adiabatic semiclassical perturbation theory for vibrationally inelastic scattering. I - Collinear calculations. II - Three-dimensional treatment

A semiclassical approximation to treat vibrationally inelastic scattering is developed. The vibrational basis set used is adiabatic with respect to a reference potential which is chosen to be as close as possible to the true potential and also gives easily obtainable solutions to the vibrational wave equation. The radial wave functions are obtained using the WKB approximation, and the coupled Schroedinger equations are solved by a first-order perturbation method to yield a phase shift matrix which is exponentiated to give the full scattering matrix. Results were obtained for all the cases computed by Secrest and Johnson and by Clark and Dickinson, and the agreement is better than 10% for half of the cross-sections and rarely off by more than a factor of 2.

Cross, R. J., Jr.↗
DOE OSTI2018

Dissipative tunnelling by means of scaled trajectories

Dissipative quantum tunnelling through an inverted parabolic barrier is considered in the presence of an electric field. A Schrödinger–Langevin or Kostin quantum–classical transition wave equation is used and applied resulting in a scaled differential equation of motion. A Gaussian wave packet solution to the resulting scaled Kostin nonlinear equation is assumed and compared to the same solution for the scaled linear Caldirola–Kanai equation. The resulting scaled trajectories are obtained at different dynamical regimes and friction cases, showing the gradual decoherence process in this open dynamics. Theoretical results show that the transmission probabilities are always higher in the Kostin approach than in the Caldirola–Kanai approach in the presence or not of an external electric field. This discrepancy should be understood due to the presence of an environment since the corresponding open dynamics should be governed by nonlinear quantum equations, whereas the second approach is issued from an effective Hamiltonian within a linear theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2017

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗
DOE OSTI2013

An Airy beam as a self-similar solution to the problem of slit laser beam propagation in a linear medium and in a photorefractive crystal with diffusion nonlinearity

We have analysed self-similar solutions to the propagation problem of a slit beam with a plane wavefront in a linear medium and in a photorefractive crystal with diffusion nonlinearity. It is shown that in the latter case, despite the presence of the nonlinear term in the wave equation, the linear superposition principle holds true for the solutions of this class due to saturation. At the same time, the mirror symmetry violation of the wave equation for the transverse coordinate in the nonlinear case and the requirement to the spatial localisation modify one of the localised partial solutions (Airy beam) to the corresponding linear problem and prohibit the existence of other solutions of this class. (laser beams)

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1989

Acoustic response of a rectangular waveguide with a strong transverse temperature gradient

An acoustic wave equation was developed for a perfect gas with spatially-variable temperature. The strong-gradient wave equation was used to analyze the response of a rectangular wave guide containing a thermally-stratified gas. It was assumed that the temperature gradient is constant, representing one-dimensional heat transfer with a constant coefficient of conductivity. The analysis of the waveguide shows that the resonant frequencies of the waveguide are shifted away from the values that would be expected from the average temperature of the waveguide. For small gradients, the frequency shift is proportional to the square of the gradient. The factor of proportionality is a quadratic function of the natural frequency of the waveguide with uniform temperature. An experiment is designed to verify the essential features of the strong-gradient theory.

Zorumski, William E.↗
NASA NTRS1980

Numerical techniques for solving nonlinear instability problems in smokeless tactical solid rocket motors

The selection of a satisfactory numerical method for calculating the propagation of steep fronted shock life waveforms in a solid rocket motor combustion chamber is discussed. A number of different numerical schemes were evaluated by comparing the results obtained for three problems: the shock tube problems; the linear wave equation, and nonlinear wave propagation in a closed tube. The most promising method--a combination of the Lax-Wendroff, Hybrid and Artificial Compression techniques, was incorporated into an existing nonlinear instability program. The capability of the modified program to treat steep fronted wave instabilities in low smoke tactical motors was verified by solving a number of motor test cases with disturbance amplitudes as high as 80% of the mean pressure.

Baum, J. D.↗
NASA NTRSDate not supplied

Evaluation of Acoustic Propagation in Layered Media Using Wave Confinement

A comprehensive method for propagation of sound in layered media is discussed that involves dividing the domain into two regions, source field and far field. The source field is provided using experimentally collected data from full-scale rotorcraft acoustic flight tests, which consists of short waveforms that cannot be directly simulated on the grid without numerical errors. Instead, grid based computational waves are used to carry the details of these waveforms, including amplitude, arrival time and location of origin on source sphere. This is done by solving the scalar wave equation using the Wave Confinement (WC) method, which involves adding an extra term to produce converged solutions. WC is used to study wave propagation in two different atmospheric conditions, and the results are compared to the flight test data. Overall, WC can accurately capture the propagation effects and there is a good agreement with the flight test data.

rotorcraft acoustics↗
NASA NTRSDate not supplied

Evaluation of Acoustic Propagation in Layered Media Using Wave Confinement

A comprehensive method for propagation of sound in layered media is discussed that involves dividing the domain into two regions, source field and far field. The source field is provided using experimentally collected data from full-scale rotorcraft acoustic flight tests, which consists of short waveforms that cannot be directly simulated on the grid without numerical errors. Instead, grid based computational waves are used to carry the details of these waveforms, including amplitude, arrival time and location of origin on source sphere. This is done by solving the scalar wave equation using the Wave Confinement (WC) method, which involves adding an extra term to produce converged solutions. WC is used to study wave propagation in two different atmospheric conditions, and the results are compared to the flight test data. Overall, WC can accurately capture the propagation effects and there is a good agreement with the flight test data.

rotorcraft acoustics↗
NASA NTRS1976

Rigid rotators

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

Source record↗
DOE OSTI2015

Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method

We develop a fourth order accurate finite difference method for solving the three-dimensional elastic wave equation in general heterogeneous anisotropic materials on curvilinear grids. The proposed method is an extension of the method for isotropic materials, previously described in the paper by Sjögreen and Petersson (2012) [11]. The method we proposed discretizes the anisotropic elastic wave equation in second order formulation, using a node centered finite difference method that satisfies the principle of summation by parts. The summation by parts technique results in a provably stable numerical method that is energy conserving. Also, we generalize and evaluate the super-grid far-field technique for truncating unbounded domains. Unlike the commonly used perfectly matched layers (PML), the super-grid technique is stable for general anisotropic material, because it is based on a coordinate stretching combined with an artificial dissipation. Moreover, the discretization satisfies an energy estimate, proving that the numerical approximation is stable. We demonstrate by numerical experiments that sufficiently wide super-grid layers result in very small artificial reflections. Applications of the proposed method are demonstrated by three-dimensional simulations of anisotropic wave propagation in crystals.

58 GEOSCIENCES↗
NASA NTRS1990

Conditions for vertical propagation of magnetoacoustic waves in an isothermal atmosphere

The propagation of magnetoacoustic waves in an isothermal atmosphere with constant gravity and uniform magnetic field of an arbitrary direction is considered. The conditions for the vertical propagation of these waves are determined by characteristic frequencies that arise in the MHD wave equation which is considered here in the limit of low-beta plasma. The obtained steady state solutions to the wave equation describe the behavior of fast and slow magnetoacoustic waves and allow defining the characteristic frequencies that separate domains of wave frequency where the sinusoidal and nonsinusoidal wave solutions are found. The particular problem of dependence of the characteristic frequencies on the density gradient as well as on the strength and direction of the uniform magnetic field are discussed. The obtained results may have important consequences on the behavior of magnetoacoustic waves in stellar atmospheres and may be found useful in studying stellar p-mode oscillations.

Musielak, Z. E.↗
NASA NTRS1990

Theory of biaxial graded-index optical fiber

A biaxial graded-index fiber with a homogeneous cladding is studied. Two methods, wave equation and matrix differential equation, of formulating the problem and their respective solutions are discussed. For the wave equation formulation of the problem it is shown that for the case of a diagonal permittivity tensor the longitudinal electric and magnetic fields satisfy a pair of coupled second-order differential equations. Also, a generalized dispersion relation is derived in terms of the solutions for the longitudinal electric and magnetic fields. For the case of a step-index fiber, either isotropic or uniaxial, these differential equations can be solved exactly in terms of Bessel functions. For the cases of an istropic graded-index and a uniaxial graded-index fiber, a solution using the Wentzel, Krammers and Brillouin (WKB) approximation technique is shown. Results for some particular permittivity profiles are presented. Also the WKB solutions is compared with the vector solution found by Kurtz and Streifer. For the matrix formulation it is shown that the tangential components of the electric and magnetic fields satisfy a system of four first-order differential equations which can be conveniently written in matrix form. For the special case of meridional modes, the system of equations splits into two systems of two equations. A general iterative technique, asymptotic partitioning of systems of equations, for solving systems of differential equations is presented. As a simple example, Bessel's differential equation is written in matrix form and is solved using this asymptotic technique. Low order solutions for particular examples of a biaxial and uniaxial graded-index fiber are presented. Finally numerical results obtained using the asymptotic technique are presented for particular examples of isotropic and uniaxial step-index fibers and isotropic, uniaxial and biaxial graded-index fibers.

Kawalko, Stephen F.↗
DOE OSTI2018

Helicity and vortex generation

In this work we have considered the generalization of the minimal coupling prescription. We have obtained the Navier–Stokes equation for the charged fluid embedded into an electromagnetic field. We have analyzed the wave feature of the fields. Wave equations for velocity and vorticity were obtained and gauge choices were discussed. We have studied the evolution of helicity and circulation from the Maxwell-type formulation for compressive fluid equations, charged in interaction with an electromagnetic field. We see that for both helicity and circulation there are terms that, in principle, can be considered as source terms or creation of circulation in the dynamics of fluids.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗