As was mentioned above, one of the main objective is to determine a complete shock wave model permitting to calculate emission line profiles formed within the shock wake. To reach this objective, the description of the absorption coefficient must take into account the line frequency dependence from the line center to the line wings. Other lines and continua of importance affecting the wing of the selected line must be also considered.
In addition, the more realistic model, taking into account not only bound-free terms but also bound-bound terms in the rate equations and the radiation transfer problem, could determine the wake cooling which have a strong influence on the resulting shock structure. Indeed, in this perspective, it would be possible to estimate the shock weakening during its propagation in the atmosphere. This point is certainly one of the most basic.
Finally, the last fundamental point concerns the turbulence shock
amplification. With a realistic radiative shock model, it would
be possible to know the correct compression rate versus the shock
Mach number for a specific gas and to elaborate a non-adiabatic
turbulence amplification model. This is the perspective for the
near future.
Acknowledgements: I would like to express my gratitude to Dr. Yu. A. Fadeyev for constructive comments and suggestions.