Physics of ablative Rayleigh–Taylor and Landau–Darrieus instabilities

Abstract

An analysis of the linear instability of Rayleigh–Taylor instability in ablation fronts and of Landau–Darrieus instability in laminar flames is performed by means of a physical model that allows for identifying the mechanisms that control the stability of both kinds of fronts. The stability behavior of each front is shown to be determined by the particular process of energy transport that drives it. The evolution of perturbations due to the instability is found to always lead to a change in the temperature gradients, but this effect gives place to a restoring force only if the driving mechanism is sensitive to this change, such as happens in ablation fronts driven by thermal conduction. In flame fronts, the driving mechanism is not sensitive to perturbations in the temperature gradient, but, instead, it is sensitive to the temperature perturbations. The latter give place to a force that induces the well known instability in the flame front even in the absence of a gravitational field. The force driving the flame instability as well as the force providing stabilization to an ablation front, are both obtained from the same theoretical framework. The stabilizing role of the lateral thermal conduction for short perturbation wavelengths is also analyzed.