Reflectionless Acoustic Waves in an Inhomogeneous Atmosphere

We study the vertical propagation of acoustic waves in a strongly inhomogeneous atmosphere. The class of monotonically varying profiles for the sound velocity, gas density, and gas pressure, for which acoustic waves can propagate with no reflection outside the framework of the classical WKB approximation, is found. This class of solutions, called reflectionless, is obtained by transforming the levels for waves in an ideal gas located in the gravity field into the Euler—Darboux—Poisson equation of a special kind, which has a solution in the form of a superposition of non-interacting waves propagating in opposite directions. It is noted that with this stratification, acoustic waves can have any frequency, in contrast to the exponential atmosphere, where the cutoff frequency is present.