Overview: In this chapter we present a brief treatment of atmospheric turbulence as it pertains to velocity fluctuations (classical turbulence), temperature fluctuations, and index of refraction fluctuations, the latter often referred to as optical turbulence. The primary objective here is to introduce various models of the power spectrum for optical turbulence that are commonly used in optical wave propagation studies. These models include the Kolmogorov power-law spectrum, Tatarskii spectrum (with inner scale parameter), von Karman spectrum (with both inner scale and outer scale parameters), and the modified atmospheric spectrum (with both inner scale and outer scale parameters). However, only the modified atmospheric spectrum features a high wave number "bump" just prior to the onset of the dissipation range that has been observed in temperature data. It has been shown that the presence of this spectral bump in the temperature spectrum induces a corresponding bump in the refractive-index spectrum that can have important consequences on various aspects of optical wave propagation through the atmosphere, particularly in regards to scintillation.
In the last section of the chapter we discuss the notion of temporal statistics for the atmosphere. Here we rely on Taylor's hypothesis of frozen turbulence to convert spatial statistics to temporal statistics based on the transverse wind speed. We use this same idea in later chapters to convert spatial statistics concerning beam wave propagation to corresponding temporal statistics. In this latter case, the shape of the phase front radius of curvature of the optical wave must also be taken into account.
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