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Additional Applications

  • Michael D. Collins
  • William L. Siegmann
Chapter

Abstract

The parabolic equation method is widely used in ocean acoustics and seismology. There are many additional applications, including a few that are covered in this chapter. The acoustic wave equation is derived from the equations of fluid mechanics by considering a small amplitude perturbation of a steady state [1]. The same approach may be used to derive linear wave equations that account for the effects of ambient flow and buoyancy. Wind often has significant effects in atmospheric acoustics. A generalization of the adiabatic mode solution is applicable to the case of small Mach number in which the effects of advection can be treated as a perturbation [2]. Internal gravity waves and acousto-gravity waves exist when the effects of buoyancy are significant [3]. A poro-elastic medium is a porous solid with fluid-filled pore spaces. The poro-elastic wave equation was originally derived by Biot using a macroscopic approach [4–7], but it has also been derived as a limiting case of the elastic wave equation for a fluid-solid conglomerate [8]. Poro-elastic media support fast compressional, slow compressional, shear, boundary, and interface waves. The fast wave corresponds to motions of the solid frame and the fluid that are in phase with each other. The slow wave, which corresponds to motions that are out of phase, is strongly attenuated by viscous effects but has been observed experimentally [9]. One of the applications of the poro-elastic parabolic equation is ocean acoustics problems involving interactions with porous sediments [10].

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Michael D. Collins
    • 1
  • William L. Siegmann
    • 2
  1. 1.Naval Research LaboratoryWashington, DCUSA
  2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

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