White-Noise and Geometrical OpticsLimits of Wigner–Moyal Equation for Beam Waves in Turbulent Media II: Two-Frequency Formulation |
| |
Authors: | Albert C Fannjiang |
| |
Institution: | (1) Department of Mathematics, University of California at Davis, Davis, CA 95616, USA |
| |
Abstract: | We introduce two-frequency Wigner distribution in the setting of parabolic approximation to study the scaling limits of the
wave propagation in a turbulent medium at two different frequencies. We show that the two-frequency Wigner distribution satisfies
a closed-form equation (the two-frequency Wigner–Moyal equation). In the white-noise limit we show the convergence of weak
solutions of the two-frequency Wigner–Moyal equation to a Markovian model and thus prove rigorously the Markovian approximation
with power-spectral densities widely used in the physics literature. We also prove the convergence of the simultaneous geometrical
optics limit whose mean field equation has a simple, universal form and is exactly solvable |
| |
Keywords: | Two-frequency Wigner distribution martingale geometrical optics turbulent media |
本文献已被 SpringerLink 等数据库收录! |