Wave Propagation m Continuous Random Media

A study is made of the way in which small random inhomogeneities in a transmission medium affect the statistical properties of a system of waves. It is shown that provided the spectral cumulants are sufficiently smooth at some initial time, a sequence of closures for the zeroth order spectral functions can be deduced which describe asymptotically the transfer of energy between wave numbers. Of particular importance is the fact that the closure equations are derived without the need to resort to ad hoc statistical assumptions. The general theory is applied to the problem of the propagation of water waves over an irregular bottom topography.