A Model for the Simulation of Atmospheric Turbulence

Abstract

A method that produces realistic simulations of atmospheric turbulence is developed and analyzed. The procedure makes use of a generalized spectral analysis, often called a proper orthogonal decomposition or the Karhunen-Loève expansion. A set of criteria, emphasizing a realistic appearance, a correct spectral shape, and non-Gaussian statistics, is selected in order to evaluate the model turbulence. An actual turbulence record is analyzed in detail providing both a standard for comparison and input statistics for the generalized spectral analysis, which in turn produces a set of orthonormal eigenfunctions and estimates of the distributions of the corresponding expansion coefficients. The simulation method utilizes the eigenfunction expansion procedure to produce preliminary time histories of the three velocity components simultaneously. As a final step, a spectral shaping procedure is then applied. The method is unique in modeling the three velocity components simultaneously, and it is found that important cross-statistical features are reasonably well-behaved. It is concluded that the model provides a practical, operational simulator of atmospheric turbulence.