The temperature and humidity fluctuations combined with turbulent mixing by wind and convection induce random changes in the air density and in the field of atmospheric refractive index in the form of optical turbules (or eddies), which is one of the most significant parameters for optical wave propagation [35—47]. Random space-time redistribution of the refractive index causes a variety of effects on an optical wave related to its temporal irradiance fluctuations (scintillations) and phase fluctuations. A statistical approach is usually used to describe both atmospheric turbulence and its various effects on optical wave propagation in the nonlinear irregular atmosphere.
Atmospheric turbulence is a chaotic phenomenon created by random temperature, wind magnitude variation, and direction variation in the propagation medium. This chaotic behavior results in index-of-refraction fluctuations. The turbulence spectrum is divided into three regions by two scale sizes [6,8,17-20]:
- ? The outer scale (or macro size) of turbulence: L0
- ? The inner scale (or micro size) of turbulence: l0
These values vary according to atmosphere conditions, distance from the ground, and other factors. The inner scale l0 is assumed to lie in the range of 1-30 mm and near the ground, it is typically observed to be around 3-10 mm, but generally increases to several centimeters with increasing altitude h. A vertical profile for the inner scale has still not been established. The outer scale L0 near the ground is usually taken to be roughly kh, where k is a constant on the order of unity. Thus, L0 is usually either equal to the height from the ground (when the turbulent cell is close to the ground) or in the range of 10-100 m or more. Vertical profile models for the outer scale have been developed based on measurements, but different models predict very different results.