Scaling Limits for Beam Wave Propagation in Atmospheric Turbulence

Description of waves that propagate through the turbulent atmosphere is a fundamental problem, for instance from the point of view of applications to communication and remote sensing. Yet, so far, very little is known about how the wave field interacts with the turbulent or multiscale nature of the refractive index which derives from the multiscale nature of the temperature fluctuations. The parabolic or forward scattering approximation leads to a random Schrödinger equation. Here, we take the parabolic wave equation as our starting point and derive a white noise approximation for this problem. We start with a description where the non-Gaussian multiscale nature of the refractive fluctuations are described by a power law spectrum with prescribed inner and outer scales and analyze the asymptotic limits corresponding respectively to a relatively large outer scale and or small inner scale. The reference scale in our modeling is taken to be the Fresnel length. A main tool used to derive the convergence to a Gaussian Markov limit is the method of multiple scales . From the white noise approximation we derive closed equations for the moments of the wave field.