One-dimensional ultrasound propagation in stratified gas

The system of hydrodynamic-type equations is derived by
two-sided distribution function for a stratified gas in gravity field and
applied to the problem of ultrasound. The theory is based on the generalized
Gross-Jackson kinetic equation, the solution of which is built by means of
locally equilibrium distribution function with different local parameters for
molecules moving "up" and "down". The problem of propagation of the sound wave
from an oscillating plane is explored. The linearized version of the obtained
system is studied and compared with other results and experiments for a wide
range of Knudsen numbers (Kn). The discrepancy with experiment in attenuation
behavior at big Kn range forced us to use generalized kinetic description
leading to the Alexeev-Boltzmann equation. Its use essentially improves the
results.