Piecewise continuous distribution function method: Fluid equations and wave disturbances at stratified gas

Wave disturbances of a stratified gas are studied. The description is built on a basis of the Bhatnagar–Gross–Krook (BGK) kinetic equation which has reduced down the level of fluid mechanics. The double momenta set is introduced inside a scheme of iterations of the equations operators, dividing the velocity space along and opposite gravity field directions. At both half-spaces the local equilibrium is supposed. As a result the momenta system is derived. It reproduces Navier–Stokes and Barnett equations at the first and second order at high collision frequencies. The homogeneous background limit gives the known results obtained by direct kinetics applications of Loyalka and Cheng as well as the recent higher momentum fluid mechanics results of Chen, Rao and Spiegel. The ground state declines from exponential at the Knudsen regime. The WBK solutions for ultrasound in exponentially stratified medium are constructed in explicit form, evaluated and plotted.