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. © 2005 Elsevier B.V. All rights reserved.

R. I. Sujith

Department of Aerospace Engineering

Astronomy

Atmospheric movements

Particles (particulate matter)

Shock waves

Upper atmosphere

velocity

FINITE AMPLITUDE

Shock formation

STELLAR ENVELOPE

STRATIFIED

Gas dynamics

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IIT Madras

Physica D: Nonlinear Phenomena

This paper presents an investigation of the nonlinear steepening of a gasdynamic disturbance propagating in a steady non-uniform base flow. The base flow is the steady compressible flow of a gas in a variable-area duct. The quasi-one-dimensional continuity, momentum and energy equations for the unsteady disturbance in homentropic flow are solved using the method of characteristics (wave front expansion technique). A closed-form solution for the slope of the disturbance at the wave front is obtained. The solution admits singularity for a compressive disturbance, which is responsible for the formation of shock in the flow. The solution is general and is applicable in any range of Mach number of the base flow. A special case of the steady gas flow in a convergent-divergent duct (C-D nozzle), where the flow makes a transition from subsonic to supersonic and vice versa, is investigated. © 2005 Cambridge University Press.

Journal of Fluid Mechanics

Nonlinear distortion of travelling waves in variable-area ducts with base flow: A quasi-one-dimensional analysis

This paper presents the effects of variable-area ducts and axial temperature gradients on the nonlinear distortion of a travelling wave. Quasi-one-dimensional continuity, momentum and energy equations for isentropic flow are solved using a wave front expansion technique. An evolution equation for the slope of the wave front is obtained. This is a nonlinear ordinary differential equation that can be integrated to obtain a solution in closed form for the slope of the wave front. The solution may admit a singularity for compression wave fronts. The analysis considers pure compression and pure expansion travelling waves. A general criterion is developed for the steepening of a compression wave front into a shock. A general formula is obtained for the location of shock formation. The effects of area variation and axial temperature gradient, and their combined effect on the nonlinear distortion of travelling waves are studied. A number of examples highlighting these effects are presented in the paper.

Nonlinear distortion of travelling waves in variable-area ducts with entropy gradients

Nonlinear spherical gravitational downfall of gas onto a solid ball: analytic and numerical results

Shock formation in the presence of entropy gradients

Linear and Nonlinear Waves

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

Journal	Data powered by TypesetPhysica D: Nonlinear Phenomena
Publisher	Data powered by TypesetElsevier
ISSN	01672789
Open Access	No