Strong scintillation spectra behind a phase screen containing large-scale anisotropic irregularities

Abstract

Using the approximation of an anisotropic statistically-homogeneous phase screen, we consider spectra of strong scintillations. Numerical calculations are made for the model of large-scale anisotropic inhomogeneities typical of the Earth’s stratosphere. The spectrum transformation is studied for the transition from weak scintillations to the asymptotic regime of strong scintillations. We show that with increasing level of the scintillations, their spectra rapidly broaden to the region of large wave numbers which exceed both the inverse internal scale of the irregularities and the inverse radius of the Fresnel zone by orders of magnitude. Notable deviations of the two-dimensional spectra from the predictions based on perturbation theory are shown to occur for scintillation variance exceeding 0.1. The obtained two-dimensional spectra of scintillations give a complete picture of the behavior of one-dimensional spectra which can be retrieved from satellite observations made for different angles between the orbit plane and the direction to the source. Vertical and horizontal one-dimensional spectra are studied in detail. Approximate algebraic formulas are derived and their validity is proved by applying them to the calculation of spectra of strong scintillations for a wide (several decades) range of the wave number values.