A Normal Mode Interpretation of a Range Dependent Parabolic Wave Equation

Abstract

Often it is possible to decompose a wave equation into vertical and horizontal components. It is useful to consider the case when the vertical dependence is completely expressed in a vertical normal mode representation. A parabolic wave equation with range dependence transforms to first order linear differential equations in a infinite dimensional Hilbert space. This permits concrete expression of complicated functions of operators and their calculation. The non-constant coefficient matrix shows range dependent vertical mode interactions and constraints on amplitudes. In this study differences and similarities between various transformed equations are explored. The proposed method also permits comparison to existing Hilbert space analysis of the system when the system is stochastic.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1990
Accession Number
ADA240967

Entities

People

  • Roger M. Oba

Organizations

  • United States Naval Research Laboratory

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acoustic Waves
  • Acoustics
  • Applied Mathematics
  • Boundaries
  • Computations
  • Concrete
  • Continuous Spectra
  • Differential Equations
  • Elastic Waves
  • Equations
  • Hilbert Space
  • Linear Differential Equations
  • Mathematics
  • New York
  • Underwater Acoustics
  • Wave Equations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Acoustical Oceanography.
  • Calculus or Mathematical Analysis

Technology Areas

  • Space