This thesis considers the long distance motion of waves in a random medium. Using the geometrical optics approximation and a stochastic limit theorem, we find evolution equations for rays and for energy correlations, in two and three dimensions.
Our equations are valid on a long distance scale, well after the focusing of rays has become significant. We construct asymptotic expansions of the two point energy correlation function in two and three dimensions.
In two dimensions we numerically solve the partial differential equation that determines the two point energy correlation function. We also perform Monte-Carlo simulations to calculate the same quantity. There is good agreement between the two solutions.
We present the solution for the two point energy correlation function obtained by regular perturbation techniques. This solution agrees with our solution until focusing becomes significant. Then our solution is valid (as shown by the Monte-Carlo simulations), while the regular perturbation solution becomes invalid.
Also presented are the equations that describe energy correlations after a wave has gone through a weakly stochastic plane layered medium.</p
