Single scattering estimates for the scintillation function of waves in random media

The energy density of high frequency waves propagating in highly oscillatory random media is well approximated by solutions of deterministic kinetic models. The scintillation function determines the statistical instability of the kinetic solution. This paper analyzes the single scattering term in the scintillation function. This is the term of the scintillation function that is linear in the power spectrum of the random fluctuations. We show that the structure of the scintillation function is already quite complicated in this simplified setting. It strongly depends on the singularity of the initial conditions for the wave field and on the correlation properties of the random medium. We obtain limiting expressions for the scintillation function as the correlation length of the random medium tends to zero. (C) 2010 American Institute of Physics. [doi: 10.1063/1.3276437]