The Correlation Structure of Randomly Oriented 1,2,....,N Dimensional Waves

Abstract

Here, a wave is defined as a periodic function in one or more dimensions. The superimposition of waves can be used to generate a Gaussian field which in turn can be used to simulate a meteorological field. For this field to resemble a natural field, the correlation structure in the Gaussian field must resemble the natural field correlation structure. For N dimensional waves of a single wavelength that are uniformly distributed with respect to phase and orientation, the homogeneous isotropic correlation can be found by integrating the one dimensional correlation weighted by the density of the N dimensional direction cosine distribution. This has been done for the sine/cosine, sawtooth, and triangular waves and graphs and equations are given. The triangular wave correlation closely resembles the sine/cosine correlation with possible implications for objective analysis. When coordinate systems are stretched and waves of different wavelengths and types are combined, a wide variety of nonhomogenous anisotropic correlation structure results.

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Document Details

Document Type
Technical Report
Publication Date
May 07, 1997
Accession Number
ADA329463

Entities

People

  • Albert R. Boehm

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algorithms
  • Bessel Functions
  • Convolution Integrals
  • Coordinate Systems
  • Equations
  • Integrals
  • Mathematics
  • Normal Distribution
  • Orientation (Direction)
  • Periodic Functions
  • Probability
  • Random Variables
  • Simulations
  • Sine Waves
  • Three Dimensional
  • Waveforms
  • Waves

Readers

  • Approximation Theory.
  • Theoretical Analysis.
  • Wave Propagation and Nonlinear Chaotic Dynamics.