A two-layered, analytically-tractable, atmospheric model applied to Earth, Mars, and Titan with sources

Abstract

This work utilizes an analytic expression for a model of acoustic propagation in a two-layered, inhomogeneous atmosphere developed by the authors. The model is used to study the atmospheres of Earth, Mars, and Titan. In particular, vertical wave propagation in these atmospheres is studied. The effect(s) of a two-layered, inhomogeneous atmosphere on vertical, acoustic propagation due to a time-harmonic, point source are examined. An adiabatic atmosphere is used for the bottom layer (troposphere) and an isothermal one for the top (stratosphere). The derived, analytic solution is expressed in terms of the acoustic pressure fluctuations. For the adiabatic layers, the solutions satisfy Bessel's equation for orders of $\chi =-3.5,-4.45$, and $-3.63$ for Earth, Mars, and Titan, respectively. The Bessel function's argument is $2\Omega \tau$, where $\Omega$ and $\tau$ are dimensionless frequency and height, respectively. For the isothermal layer, the solution represents a damped, harmonic oscillator with a cutoff value of ${\Omega }_c$. Only values greater than ${\Omega }_c$ are considered. The analysis and results are reported for combinations of single- and double-layer atmospheres in the presence of a source on given boundaries. Acoustic propagation and transmission loss results are shown and discussed for all three planetary bodies: Earth, Mars, and Titan.