Anomalous Reflections Near a Caustic

Abstract

We consider scattering associated to the reduced scalar wave equation. High frequency asymptotic solutions of this equation leads to the theory of geometrical optics. In this theory energy is transported along rays (orthogonal trajectories to wavefronts). However this theory breaks down as soon as the ray field forms an envelope called a caustic. This signals that a dramatic change in nature of wave propagation occurs in the vicinity of a caustic. To illustrate this change of character we study an experiment which shows that reflected waves may have arbitrarily high energy content relative to the "size" of the scatterer. Moreover a theorem is proved showing that this unbounded behaviour can only occur when a caustic develops.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 1995
Accession Number
ADA445644

Entities

People

  • Clifford J. Nolan
  • William W. Symes

Organizations

  • Rice University

Tags

DTIC Thesaurus Topics

  • Abstracts
  • Applied Mathematics
  • Energy
  • Equations
  • Frequency
  • High Energy
  • Information Operations
  • Mathematics
  • Physics
  • Reflection
  • Scattering
  • Wave Equations
  • Wave Propagation

Readers

  • Atmospheric Science / Meteorology, specifically Wind Wave Turbulence.
  • Graph Algorithms and Convex Optimization.
  • Wave Propagation and Nonlinear Chaotic Dynamics.