Real turbulence in .NET

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FIGURE 6.22. The area of scattering modeled by a disk.
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correlation length of irradiance uctuations, and the scattering disk characterizes the width of the residual tail: x=r0 k. In References [46 48], the theory developed in References [43,44] was modi ed for strong uctuations and showed why the smallest scales of irradiance uctuations persist into the saturation regime. The basic qualitative arguments presented in these works are still valid. Kolmogorov theory assumes that turbulent eddies range in size from a macroscale to a microscale, forming a continuum of decreasing eddy sizes. The largest eddy-cell size, smaller than that at which turbulent energy is injected into a region, de nes an effective outer scale of turbulence L0 , which near the ground is roughly comparable with the height of the observation point above ground. An effective inner scale of turbulence l0 is associated with the smallest cell size before energy is dissipated into heat. We will brie y present modi cations of the Rytov method obtained in References [46 48] to develop a relatively simple model for irradiance uctuations, that is, applicable in moderate-to-strong uctuation regimes. In References [46 48], the following basic observations and assumptions have been stated: atmospheric turbulence affects a propagating wave as statistically inhomogeneous structure; the received irradiance of a wave can be modeled as a modulation process in which small-scale (diffractive) uctuations are multiplicatively modulated by large scale (refractive) uctuations; small-scale processes and large-scale processes are statistically independent; the Rytov method for signal intensity scintillation is valid even into the saturation regime with the introduction of a spatial frequency lter to account properly for the loss of spatial coherence of the wave in strong- uctuation regimes; the geometrical-optics method can be applied to large-scale irradiance uctuations. These observations and assumptions are based on recognizing that the distribution of refractive power among the turbulent eddy cells of a random medium is described by an inverse power of the physical size of the cell. Thus, the large turbulent cells act as refractive lenses with focal lengths typically on the order of hundreds of meters or more, creating the so-called focusing effect or refractive scattering (Fig. 6.23a). This kind of scattering is de ned by the coherent component of the total signal passing the troposphere. The smallest cells have the weakest refractive power and the largest cells the strongest. As a coherent wave begins to propagate into a random atmosphere, the wave is scattered by the smallest of the turbulent cells (on the order of millimeters) creating the so-called defocusing effect or diffractive scattering (see Fig. 6.23b). This kind of scattering is de ned by the incoherent component of the total signal. Thus, they act as defocusing lenses, decreasing the amplitude of the wave by a signi cant amount, even for short propagation distances. The diffractive scattering spreads the wave as
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FIGURE 6.23(a). The focusing effect.
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FIGURE 6.23(b). The defocusing effect.
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it propagates. Refractive and diffractive scattering processes are compound mechanisms, and the total scattering process acts like a modulation of small-scale uctuations by large-scale uctuations. Schematically, such a situation is sketched in Figure 6.24 containing both components of the total eld. Small-scale contributions p to scintillation are associated with turbulent cells smaller than the Fresnel zone x=k or the coherence radius r0 , whichever is smaller. Large-scale uctuations in the irradiance are generated by turbulent cells larger than that of the rst Fresnel zone or the scattering disk x=kr0 , whichever is larger, and can be described by the method of geometrical optics. Under strong- uctuation conditions, spatial cells having size between those of the coherence radius and the scattering disk contribute little to scintillation. Hence, because of the loss of spatial coherence, only the very largest cells near the transmitter have focusing effect on the illumination of small diffractive cells near the receiver. Eventually, even these large cells cannot focus or defocus. When this loss of coherence happens, the illumination of the small cells is (statistically) evenly distributed and the uctuations of the
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