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.