The Correlation Structure of Randomly Oriented 1,2,....,N Dimensional Waves
Scientific rept. no. 6
HUGHES STX CORP LANHAM MD
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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 sinecosine, sawtooth, and triangular waves and graphs and equations are given. The triangular wave correlation closely resembles the sinecosine 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.
- Operations Research