The propagation of finite amplitude gasdynamic disturbances in a stratified atmosphere around a celestial body: An analytical study

This paper investigates the nonlinear distortion of a finite amplitude gasdynamic disturbance propagating outward/inward in the atmosphere of a celestial body. The Euler equations for isentropic flow considering the effect of gravitational field of the celestial body are solved for a spherically symmetric disturbance. A nonlinear ordinary differential equation for the evolution of a propagating wave front is obtained. This equation can be integrated to obtain a closed form solution for the slope of unsteady particle velocity at the wave front. Using this solution the nonlinear steepening of compression waves into shocks and nonlinear relaxing of expansion waves are analyzed.