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Wave And Extra Wide Angle Parabolic Equations For Sound Propagation In A Moving Atmosphere
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Book Synopsis Wave and Extra-wide-angle Parabolic Equations for Sound Propagation in a Moving Atmosphere by : Vladimir E. Ostashev
Download or read book Wave and Extra-wide-angle Parabolic Equations for Sound Propagation in a Moving Atmosphere written by Vladimir E. Ostashev and published by . This book was released on 2020 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The narrow-angle parabolic equation (NAPE) with the effective sound speed approximation (ESSA) is widely used for sound and infrasound propagation in a moving medium such as the atmosphere. However, it is valid only for angles less than 20° with respect to the nominal propagation direction. In this paper, the wave equation and extra-wide-angle parabolic equation (EWAPE) for high-frequency (short-wavelength) sound waves in a moving medium with arbitrary Mach numbers are derived without the ESSA. For relatively smooth variations in the medium velocity, the EWAPE is valid for propagation angles up to 90°. Using the Padé (n,n) series expansion and narrow-angle approximation, the EWAPE is reduced to the wide-angle parabolic equation (WAPE) and NAPE. Versions of these equations are then formulated for low Mach numbers, which is the case that is usually considered in the literature. The phase errors pertinent to the equations considered are studied. It is shown that the equations for low Mach numbers and the WAPE with the ESSA are applicable only under rather restrictive conditions on the medium velocity. An effective numerical implementation of the WAPE for arbitrary Mach numbers in the Padé (1,1) approximation is developed and applied to sound propagation in the atmosphere.
Book Synopsis Solution of Wide-angle Parabolic Equations for Long-range Sound Propagation in a Moving Medium by : David Keith Wilson
Download or read book Solution of Wide-angle Parabolic Equations for Long-range Sound Propagation in a Moving Medium written by David Keith Wilson and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Parabolic Wave Equations with Applications by : Michael D. Collins
Download or read book Parabolic Wave Equations with Applications written by Michael D. Collins and published by Springer Nature. This book was released on 2019-11-04 with total page 135 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces parabolic wave equations, their key methods of numerical solution, and applications in seismology and ocean acoustics. The parabolic equation method provides an appealing combination of accuracy and efficiency for many nonseparable wave propagation problems in geophysics. While the parabolic equation method was pioneered in the 1940s by Leontovich and Fock who applied it to radio wave propagation in the atmosphere, it thrived in the 1970s due to its usefulness in seismology and ocean acoustics. The book covers progress made following the parabolic equation’s ascendancy in geophysics. It begins with the necessary preliminaries on the elliptic wave equation and its analysis from which the parabolic wave equation is derived and introduced. Subsequently, the authors demonstrate the use of rational approximation techniques, the Padé solution in particular, to find numerical solutions to the energy-conserving parabolic equation, three-dimensional parabolic equations, and horizontal wave equations. The rest of the book demonstrates applications to seismology, ocean acoustics, and beyond, with coverage of elastic waves, sloping interfaces and boundaries, acousto-gravity waves, and waves in poro-elastic media. Overall, it will be of use to students and researchers in wave propagation, ocean acoustics, geophysical sciences and more.
Book Synopsis Atmospheric Sound Propagation Using the Wide-angle Parabolic Equation by : P. Malbéqui
Download or read book Atmospheric Sound Propagation Using the Wide-angle Parabolic Equation written by P. Malbéqui and published by . This book was released on 1996 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Ocean Acoustic Propagation in Three Dimensions by : Ding Lee
Download or read book Numerical Ocean Acoustic Propagation in Three Dimensions written by Ding Lee and published by World Scientific. This book was released on 1995 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a comprehensive mathematical formulation of the three-dimensional ocean acoustic propagation problem by means of functional and operator splitting techniques in conjunction with rational function approximations. It presents various numerical solutions of the model equation such as finite difference, alternating direction and preconditioning. The detailed analysis of the concept of 3D, N x 2D and 2D problems is very useful not only mathematically and physically, but also computationally. The inclusion of a complete detailed listing of proven computer codes which have been in use by a number of universities and research organizations worldwide makes this book a valuable reference source. Advanced knowledge of numerical methods, applied mathematics and ocean acoustics is not required to understand this book. It is oriented toward graduate students and research scientists to use for research and application purposes.
Book Synopsis Fast Parabolic Approximations for Acoustic Propagation in the Atmosphere by :
Download or read book Fast Parabolic Approximations for Acoustic Propagation in the Atmosphere written by and published by . This book was released on 1995 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Parabolic equations can be used to find approximate solutions to the reduced wave equation. By reducing the equation to first order in the range derivative, the solution can be found by marching forward in range. Several numerical techniques can be applied to the solution of the parabolic equation (PE), including finite elements, finite differences, and a Fourier Transform method known as the split-step PE. The split-step solves for each range increment in two steps. First, it propagates forward through a homogenous atmosphere, using the Fourier Transform. It then applies a multiplicative phase correction for index-of-refraction variations. The split-step method leads to a computationally fast model for two reasons: the range steps are several wavelengths, and the Fourier Transform can be evaluated by a Fast Fourier Transform. One of the difficulties encountered in applying the split-step PE to outdoor sound propagation is accommodation of the complex ground impedance. The Green's function PE is a split-step PE which solves for the one-dimensional height-dependant Green's function in a homogenous atmosphere. This Green's function incorporates the complex ground impedance as a complex, angle-dependant plane-wave reflection coefficient. (AN).
Book Synopsis Wave Propagation and Underwater Acoustics by : Joseph Bishop Keller
Download or read book Wave Propagation and Underwater Acoustics written by Joseph Bishop Keller and published by Springer. This book was released on 1977 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Development of the Modern Theory of Sound Propagation in the Turbulent Atmosphere by :
Download or read book Development of the Modern Theory of Sound Propagation in the Turbulent Atmosphere written by and published by . This book was released on 1998 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The foundations of the modern theory of sound propagation and scattering in a homogeneous and isotropic atmospheric turbulence are developed: The sound scattering cross-section for von Karman spectra of temperature and wind velocity fluctuations is calculated; the rigouros theory of line of sight sound propagation in an atmosphere with Kolmogorov, Gaussian and von Karman spectra of temperature and wind velocity fluctuations is developed; a new theoretical formulation of the interference of the direct wave from source to receiver and that reflected from the ground in a turbulent atmosphere is presented; the sound scattering cross section in an atmosphere with arbitrary profiles of temperature and wind velocity is calculated; some predictions of the modern theory are verified experimentally; correct wideangle parabolic equations for sound waves in a turbulent atmosphere are derived and used for numerical simulations of sound propagation. The modern theory has already been adopted by scientists for calculations of sound propagation in turbulent media and as a basis for development of new acoustic remote sensing techniques of the atmosphere and ocean in several countries and organizations including the U.S. Army Research Laboratory.
Book Synopsis Evaluation of Improvements to an Underwater Acoustic Propagation Model Based on the Parabolic Equation by : Kirk A. Weatherly
Download or read book Evaluation of Improvements to an Underwater Acoustic Propagation Model Based on the Parabolic Equation written by Kirk A. Weatherly and published by . This book was released on 2000-06 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis examines two implementations of the parabolic equation approximation to the acoustic wave equation aimed at removing three errors inherent to the wide-angle parabolic equation (WAPE) model. First, the selection of the range step size used by the split-step Fourier algorithm affects the convergence of the solution. Second, in certain ocean environments WAPE incorrectly computes the down-range transmission loss. Finally, WAPE does not reproduce the standard normal mode basis set as defined by normal mode theory. A double-precision implementation of the WAPE (DP-WAPE) is developed to evaluate the dependence of solution convergence on the numerical precision of the model. Finally, an implementation that is insensitive to the choice of the reference sound speed (COIPE) is evaluated for its ability to reduce or remove the latter two of these three errors. The stability other WAPE solution was found to be unaffected by the DP-WAPE implementation. The range-step dependence is inherent to the split-step algorithm. The COIPE corrects the transmission loss anomaly and satisfactorily reproduces the standard normal mode basis set.
Book Synopsis Application of the Parabolic Equation to Sound Propagation in a Refractive Atmosphere by : Michael James White
Download or read book Application of the Parabolic Equation to Sound Propagation in a Refractive Atmosphere written by Michael James White and published by . This book was released on 1988 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Springer Handbook of Acoustics by : Thomas Rossing
Download or read book Springer Handbook of Acoustics written by Thomas Rossing and published by Springer Science & Business Media. This book was released on 2007-06-21 with total page 1179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an unparalleled modern handbook reflecting the richly interdisciplinary nature of acoustics edited by an acknowledged master in the field. The handbook reviews the most important areas of the subject, with emphasis on current research. The authors of the various chapters are all experts in their fields. Each chapter is richly illustrated with figures and tables. The latest research and applications are incorporated throughout, including computer recognition and synthesis of speech, physiological acoustics, diagnostic imaging and therapeutic applications and acoustical oceanography. An accompanying CD-ROM contains audio and video files.
Book Synopsis Equations for Finite-Difference, Time-Domain Simulation of Sound Propagation in Moving Inhomogeneous Media and Numerical Implementation by :
Download or read book Equations for Finite-Difference, Time-Domain Simulation of Sound Propagation in Moving Inhomogeneous Media and Numerical Implementation written by and published by . This book was released on 2005 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite-difference, time-domain (FDTD) calculations are typically performed with partial differential equations that are first order in time. Equation sets appropriate for FDTD calculations in a moving inhomogeneous medium with an emphasis on the atmosphere! are derived and discussed in this paper. Two candidate equation sets, both derived from linearized equations of fluid dynamics, are proposed. The first, which contains three coupled equations for the sound pressure, vector acoustic velocity, and acoustic density, is obtained without any approximations. The second, which contains two coupled equations for the sound pressure and vector acoustic velocity, is derived by ignoring terms proportional to the divergence of the medium velocity and the gradient of the ambient pressure. It is shown that the second set has the same or a wider range of applicability than equations for the sound pressure that have been previously used for analytical and numerical studies of sound propagation in a moving atmosphere. Practical FDTD implementation of the second set of equations is discussed. Results show good agreement with theoretical predictions of the sound pressure due to a point monochromatic source in a uniform, high Mach number flow and with Fast Field Program calculations of sound propagation in a stratified moving atmosphere.
Book Synopsis Outdoor Sound Propagation Modelling in Complex Environments: Recent Developments in the Parabolic Equation Method by :
Download or read book Outdoor Sound Propagation Modelling in Complex Environments: Recent Developments in the Parabolic Equation Method written by and published by . This book was released on 2006 with total page 17 pages. Available in PDF, EPUB and Kindle. Book excerpt: In complex environments the modelling of outdoor sound propagation implies to take into account the mixed influence of ground characteristics (topography, obstacles, impedance, etc.) and atmospheric conditions (refraction and turbulence). During the last decade significant progress has been made in the modelling of sound propagation over distances ranging from hundreds meters to kilometres, and the agreement between calculated and measured fields has been greatly improved. New developments appear in the parabolic-equation method. In this paper we present a method which evaluates the propagation of an acoustic wave above uneven terrains including realistic meteorological parameters. In our approach the effects of the topography are modelled using appropriate rotated co-ordinates systems in order to treat the non-flat ground as a succession of flat domains. We also examine the influence of scale resolution on numerical simulation of long range sound propagation through the turbulent atmosphere. Currently, we generate the turbulence using a Random Fourier Modes technique, such that the turbulent fluctuation at any point in the medium (either scalar or vectorial in nature) is calculated from the sum of a chosen number of modes. Our model of outdoors sound propagation is validated both with classical numerical benchmark cases and recent outdoor experiments.
Book Synopsis Linear and Nonlinear Acoustic Wave Propagation in the Atmosphere by : S. I. Hariharan
Download or read book Linear and Nonlinear Acoustic Wave Propagation in the Atmosphere written by S. I. Hariharan and published by . This book was released on 1988 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Nonlocal Tops and Equivalent Bottoms for Sound Propagation in Air Problems by :
Download or read book Nonlocal Tops and Equivalent Bottoms for Sound Propagation in Air Problems written by and published by . This book was released on 1999 with total page 2 pages. Available in PDF, EPUB and Kindle. Book excerpt: One-way wave equations derived from the parabolic equation (PE) approximation are widely used to model underwater & atmospheric sound propagation. To solve a PE numerically, the computational grid must be terminated top & bottom. In outdoor sound applications, the acoustic field is usually assumed to satisfy a constant-impedance boundary condition along the ground plane, a condition easily incorporated into finite-difference PE models. However, wavenumber integration codes such as SAFARI, developed specifically for underwater sound propagation applications, do not incorporate this condition directly. The first part of this paper designs an equivalent fluid whose reflection response is numerically equivalent to that produced by a constant-impedance surface. The second part presents a non-local boundary condition (NLBC) that exactly transforms the semi-infinite PE problem with a radiation condition at infinite height into an equivalent PE problem in a bounded domain. A numerical example is provided that compares SAFARI predictions obtained with an equivalent bottom to PE predictions obtained with a NLBC top for a problem that typifies outdoor sound propagation.
Book Synopsis The Use of the Parabolic Equation Method in Sound Propagation Modelling by : Finn Jensen
Download or read book The Use of the Parabolic Equation Method in Sound Propagation Modelling written by Finn Jensen and published by . This book was released on 1975 with total page 50 pages. Available in PDF, EPUB and Kindle. Book excerpt: The parabolic equation method (PE method) is the latest major development in the field of acoustic modelling. A detailed description of the derivation of the parabolic equation from the wave equation is given together with a description of a marching solution technique based on Fast Fourier Transforms (FFT). Limitations on the method in terms of allowable step length in range, number of FFT points to be used, and restrictions on pressure field behaviour in order to obtain a stable solution, are mentioned. Furthermore, numerical examples of propagation predictions are given for both shallow and deep water cases, with and without bottom absorption, and for both range-dependent and range-independent environmental conditions.
Book Synopsis On the Propagation of Atmospheric Gravity Waves in a Non-uniform Wind Field by : Ahmad Talaei
Download or read book On the Propagation of Atmospheric Gravity Waves in a Non-uniform Wind Field written by Ahmad Talaei and published by . This book was released on 2016 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Atmospheric gravity waves play fundamental roles in a broad-range of dynamical processes extending throughout the Earth0́9s neutral atmosphere and ionosphere. In this paper, we present a modified form for the acoustic-gravity wave equation and its dispersion relationships for a compressible and non-stationary atmosphere in hydrostatic balance. Importantly, the solutions have been achieved without the use of the well-known Boussinesq approximation which have been used extensively in previous studies. We utilize the complete set of governing equations for a compressible atmosphere with non-uniform airflows to determine an equation for vertical velocity of possible atmospheric waves. This intricate wave equation is simplified by a proper substitution producing a useful new wave-like equation for acoustic-gravity waves. The substitution introduces a term omega (intrinsic frequency) in the amplitude of the wave solution for the vertical velocity of acoustic-gravity waves. This term may play a significant role in directional filtering of atmospheric waves in realistic atmospheres exhibiting strong and highly variable winds. It is also proven that the only difference in the wave equation of compressible fluid when non-uniform wind is added to the equations of motion is the term with second derivative of Ln(omega) with respect to height. These new solutions may be particularly important for improved gravity wave propagation studies in the upper mesosphere and thermosphere/ionosphere regions.
