Discrete, Continuous, and Virtual Modes in Underwater Sound Propagation

Abstract

Adopting two physical postulates and using only the language of eigenfunctions and eigenvalues, the author expresses the underwater sound field of a harmonic point source as a sum over orthonormal discrete modes plus an integral over a continuous set of normal modes. Restrictions are constant water depth, no absorption, parameters varying only with depth, and bottom material treated as a fluid. For the Pekeris case, orthogonality of the continuous modes is demonstrated, and the integral over continuous modes is proved identical to the branch line integral (BLI) of Ewing, Jardetzky, and Press. It is shown that farfield contributions to BLI are practically negligible except for contributions from narrow 'spikes' or resonances of the integrand. Conditions for existence of resonances are stated.

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Document Details

Document Type
Technical Report
Publication Date
Aug 26, 1976
Accession Number
ADA033084

Entities

People

  • A. O. Williams Jr.

Organizations

  • University of Texas at Austin

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Acoustic Waves
  • Acoustics
  • Computers
  • Eigenvalues
  • Elastic Waves
  • Equations
  • Frequency
  • Integrals
  • Physics Laboratories
  • Reflection
  • Standing Waves
  • Underwater Acoustics
  • Underwater Sound
  • Universities
  • Wave Equations
  • Waves
  • Weighting Functions

Readers

  • Approximation Theory.
  • Electromagnetic Wave Scattering and Antenna Radiation Engineering
  • Fluid Dynamics.