William L. Siegmann

Bio: William L. Siegmann is an academic researcher from Rensselaer Polytechnic Institute. The author has contributed to research in topics: Parabolic partial differential equation & Internal wave. The author has an hindex of 18, co-authored 172 publications receiving 1213 citations.

Measurement and modeling of three-dimensional sound intensity variations due to shallow-water internal waves

Abstract: Broadband acoustic data (30–160 Hz) from the SWARM’95 experiment are analyzed to investigate acoustic signal variability in the presence of ocean internal waves. Temporal variations in the intensity of the received signals were observed over periods of 10 to 15 min. These fluctuations are synchronous in depth and are dependent upon the water column variability. They can be explained by significant horizontal refraction taking place when the orientation of the acoustic track is nearly parallel to the fronts of the internal waves. Analyses based on the equations of vertical modes and horizontal rays and on a parabolic equation in the horizontal plane are carried out and show interesting frequency-dependent behavior of the intensity. Good agreement is obtained between theoretical calculations and experimental data.

Examination of three-dimensional effects using a propagation model with azimuth-coupling capability (FOR3D)

Abstract: A three‐dimensional wave propagation model of parabolic approximation type (FOR3D) is used to examine 3‐D ocean environmental variations. The background theory and characteristics of the model are reviewed briefly. Propagation situations that are classified as 3‐D, N×2‐D, and 2‐D are described in connection with FOR3D and are interpreted in several ways. An analytic exact solution is used to demonstrate the model’s accuracy and its capability for treating fully 3‐D propagation, when coupling exists between solutions in adjacent vertical planes of constant azimuth. It is also employed to illustrate a procedure for using approximate conditions at vertical side boundaries in a 3‐D calculation. An application is made to an Atlantic Ocean shelf‐slope environment with realistic bottom topographic variations and sound‐speed profiles. The occurrence of significant azimuthal coupling is demonstrated in propagation loss versus range curves. It follows that, while the N×2‐D approximation of no azimuthal coupling is ...

Internal waves in a rotating stratified fluid in an arbitrary gravitational field

Abstract: Small amplitude oscillations of a uniformly rotating, density stratified, Boussinesq, non-dissipative fluid are examined. A mathematical model is constructed to describe timedependent motions which are small deviations from an initial state that is motionless with respect to the rotating frame of reference. The basic stable density distribution is allowed to be an arbitrary prescribed function of the gravitational potential. The problem is considered for a wide class of gravitational fields. General properties of the eigenvalues and eigenfunctions of square integrable oscillations are demonstrated, and a bound is obtained for the magnitude of the frequencies. The modal solutions are classified as to type. The eigenfunctions for the pressure field are shown to satisfy a second-order partial differential equation of mixed type, and the equation is obtained for the critical surfaces which delineate the elliptic and hyperbolic regions. The nature of the problem is examined in detail for certain speci...

A wide‐angle three‐dimensional parabolic wave equation

Abstract: A third‐order partial differential equation with wide‐angle capability is formulated to predict three‐dimensional underwater sound propagation. The development is based on physical acoustic characteristics and mathematical theory. Both operator and asymptotic analyses are given to thoroughly discuss the validity of the formulation. Physical conditions are indicated when a three‐dimensional approach is needed.

Modeling Rayleigh and Stoneley waves and other interface and boundary effects with the parabolic equation.

Abstract: An improved approach for handling boundaries, interfaces, and continuous depth dependence with the elastic parabolic equation is derived and benchmarked. The approach is applied to model the propagation of Rayleigh and Stoneley waves. Depending on the choice of dependent variables, the operator in the elastic wave equation may not factor or the treatment of interfaces may be difficult. These problems are resolved by using a formulation in terms of the vertical displacement and the range derivative of the horizontal displacement. These quantities are continuous across horizontal interfaces, which permits the use of Galerkin's method to discretize in depth. This implementation extends the capability of the elastic parabolic equation to handle arbitrary depth dependence and should lead to improvements for range-dependent problems.

Methods of Mathematical Physics. By Harold Jeffreys and Bertha Swirles Jeffreys. Pp. viii, 679. 63s. 1946. (Cambridge University Press)

Abstract: 1. The real variable 2. Scalars and vectors 3. Tensors 4. Matrices 5. Multiple integrals 6. Potential theory 7. Operational methods 8. Physical applications of the operational method 9. Numerical methods 10. Calculus of variations 11. Functions of a complex variable 12. Contour integration and Bromwich's integral 13. Contour integration 14. Fourier's theorem 15. The factorial and related functions 16. Solution of linear differential equations of the second order 17. Asymptotic expansions 18. The equations of potential, waves and heat conduction 19. Waves in one dimension and waves with spherical symmetry 20. Conduction of heat in one and three dimensions 21. Bessel functions 22. Applications of Bessel functions 23. The confluent hypergeometric function 24. Legendre functions and associated functions 25. Elliptic functions Notes Appendix on notation Index.

Global morphology of infrasound propagation

Abstract: [i] Atmospheric sound waves in the 0.02-10 Hz region, also known as infrasound, exhibit long-range global propagation characteristics. Measurable infrasound is produced around the globe on a daily basis by a variety of natural and man-made sources. As a result of weak classical attenuation (∼0.01 dB km -1 at 0.1 hz), these acoustic signals can propagate thousands of kilometers in tropospheric, stratospheric, and lower thermospheric ducts. To model this propagation accurately, detailed knowledge of the background atmospheric state variables, the global winds and temperature fields from the ground to ∼170 km, is required. For infrasound propagation calculations, we have developed a unique atmospheric specification system (G2S) that is capable of providing this information. Using acoustic ray tracing methods and detailed G2S atmospheric specifications, we investigate the major aspects of the spatiotemporal variability of infrasound propagation characteristics.

An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment

Abstract: An overview is given of the July-August 1995 SWARM shallow-water internal wave acoustic scattering experiment. This experiment studied both acoustic propagation through and scattering by the linear and nonlinear internal waves found on the Mid-Atlantic Bight continental shelf, as well as the physical oceanography of the internal wavefield. In order that their goal of explaining the nature of the acoustic scattering should not be hindered by incomplete environmental knowledge, numerous instruments, both ship-deployed and moored, measured the acoustics, geophysics, and oceanography. In this paper, the authors show some of the results from the first year's analysis of the environmental and acoustic data. The environmental measurements, which are a key input to the analyses of the acoustic data, are given slightly more emphasis at this point in time. Some of the more interesting oceanographic, geophysical, and acoustical results the authors present are: evidence for the dominance of the lee-wave mechanism for soliton production, evidence for the "solibore internal tide" the "dnoidal wave" description of solitons, the inversion of chirp sonar data for bottom properties, propagation loss extraction from air-gun data, and the intensity and travel-time fluctuations seen in propagating acoustic normal modes. Directions for future research are outlined.