EULER-LAGRANGE RELATIONSHIP FOR RANDOM DISPERSIVE WAVES,

Abstract

It is shown that the equations for the motion of a tagged fluid particle in a random wave field define a singular perturbation problem, characterized by a non-uniformity at large times. The uniformly valid asymptotic expansion to this problem, the Euler-Lagrange relationship for random dispersive waves, is obtained. As an application of these general results, an integral representation of the solution is worked out for the case of vertically propagating random acoustic waves in an isothermal atmosphere. It is shown that the non-uniformity of mediums leads to a wave generated diffusion process. The time and length scales over which the process is diffusive are determined, and a formula for the diffusion coefficient is presented. (Author)

Document Details

Document Type
Technical Report
Publication Date
Apr 01, 1968
Accession Number
AD0673511

Entities

People

  • D. P. Hoult

Organizations

  • Pennsylvania State University

Tags

Communities of Interest

  • Materials and Manufacturing Processes

DTIC Thesaurus Topics

  • Acoustic Waves
  • Asymptotic Series
  • Atmospheres
  • Coefficients
  • Diffusion
  • Diffusion Coefficient
  • Equations
  • Integrals
  • Mathematics
  • Particles
  • Perturbations
  • Waves

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Fluid Dynamics.
  • Wave Propagation and Nonlinear Chaotic Dynamics.