Modeling two-point spatial turbulence spectra for analysis of gust variations over aerospace vehicles

Analytical models for two-point spatial spectra of atmospheric turbulence axe developed. Models based on both the von Karman and Dryden correlation are presented. A two-point auto-correlation, defined as the correlation between like components of velocity measured at two spatially separated positions, is Fomier transformed to give the spectrum. The bias and aliasing errors associated with fast Fourier transform techniques for two-point spatial correlations are described. A comparison is given of the spectrum computed by the fast Fourier transform of the digitized analytical correlation, with closed form solutions. The results demonstrate that the two-point spatial spectrum is extremely sensitive to bias errors. Filters for smoothing the data to minimize the bias error axe investigated and an optimum filter is proposed.