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The outer scale length is 1 proportional to E 2 . This means that the inertial range should broaden as the energy rate rises, with 0 decreasing and L0 increasing. It was soon realized that the same techniques could be applied to describe the turbulent mixing of a passive scalar [14][15][16]. 6: A wavenumber spectrum for refractive-index ﬂuctuations showing three distinct stages of the turbulence process. The inertial-range behavior is the only speciﬁc prediction in this diagram. Descriptions for the other regions are only suggestive at this point.

The Fresnel length λR is the fundamental length scale when diffraction effects are important. It is comparable to 0 for short paths and optical wavelengths. 2 By contrast, the Fresnel length is always large relative to 0 for microwave frequencies and one need not include this correction in their description. Phase measurements depend primarily on large eddies and are insensitive to the dissipation region. Angle-of-arrival and image-centroid fluctuations lie midway between amplitude and phase measurements.

A Gaussian model A popular description of the dissipation range is based on the Gaussian model. 65) This analytical model dominated studies of random media for three decades, primarily because the ensuing propagation integrations can usually be done in closed form. It is often referred to as the Tatarskii model because he was the first to use it extensively [17]. One should note that he was well aware of its limitations and observed that it did not agree with actual measurements then in hand. 66) The product ρκm is very large when the separation is greater than the inner scale length.

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