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Response to the comment on instabilities of intense shock waves in monatomic gases

Published online by Cambridge University Press:  31 January 2002

R. ANNOU
Affiliation:
Theoretical Physics Laboratory, The Physics Institute, USTHB, BP 32 El Alia, Algiers 16111, Algeria

Abstract

We respond here to the comment by Houili et al. (2001) on our paper on instabilities of intense shock waves in monatomic gases (Annou and Ferhat 1997).

It has been reported that a strong shock-wave front in a shock tube, ceases to be plane and becomes distorted for particular experimental conditions (Schreffler and Christian 1954). Two different approaches have been developed to explain the instability (Annou 1995; Annou and Ferhat 1997). By means of the macroscopic approach, we can reproduce the experimental data. Nonetheless, many parameters suspected to be at the root of the instability have not been taken into account. Consequently, a microscopic approach has been proposed that copes with the atomic reactions taking place due to the shock wave. An irreducible system of atomic reactions leading to ionization of the gas is proposed. This is an attempt to develop a mathematical tool that has to be improved to account for the front distortion. A system of two nonlinear differential equations is obtained. As a matter of fact, we have been greatly inspired by the Brusselator model. Our achievement has been to link the experimental data to a reaction-diffusion equation system, analogous to the Brusselator. Hence, the analytical treatment of the stability, along with finding the solution beyond the instability, is based on the work of Nicolis and Prigogine (1977). It should be noted, as well, that the paper by Annou and Ferhat (1997) is based essentially on a thesis submitted (1994) for the award of the Magister degree (Annou 1995).One of the authors of the paper (R.A.) had asked Mr Houili to investigate the system numerically, and provided him with the necessary literature. Unfortunately, the comment was submitted for publication without consulting either of the authors of the original paper.

Type
Research Article
Copyright
2001 Cambridge University Press

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