A comparison of spectral models used in developing non-Kolmogorov Wave Structure Functions

We compare the Wave Structure Function (WSF) resulting from various models for refractive index fluctuation spectra in non-Kolmogorov turbulence. Closed form, analytical expressions for the WSF based on the generalized Kolomogorov, von Kármán, analytical, and exponential models are presented and compared. We find that the generalized von Kármán model is essentially identical to the WSF resulting from numerical integration of the Analytic spectrum at separations larger than the inner scale. In addition, we demonstrate that certain approximations to the Analytic model introduce significant inaccuracies at separations as small as a hundredth of the outer scale size. Asymptotic expressions for the WSF and phase variance in non-Kolmogorov turbulence with a finite outer scale are also presented.