The calculation of the fine structure in two-dimensional periodic flows in a compressible atmosphere

Based on a linearized system of fundamental equations for the mechanics of compressible and heterogeneous fluids and gases, including an equation of state for the medium, methods from the theory of singular perturbation theory are used to compute complete dispersion relations for periodic flows. Regular components of the solution describe waves and, in limiting transitions, are reduced to known relationships from linear wave theory. Singular solutions inherent to all wave types – acoustic and gravitational – characterize ligaments that form the fine-scale structure of a heterogeneous medium. These singularities are lost as one moves towards idealized environments.