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.

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration

“…(13) to (16), are settled. The linear evolution of the perturbation amplitude in this latter phase can be described by the following equation of motion for the perturbation amplitude [26][27][28][29][30][31][32][33][35][36][37][55][56][57][58][59][60]: where g = du/dt and it will be taken as a constant g = g0. Syy is the normal component of the perturbation of the deviatoric part S,j of the stress tensor <7,;-= -p&ij + Sjj (p is the thermodynamic pressure and is Kronecker delta).…”

Rayleigh-Taylor stability boundary at solid-liquid interfaces

“…Thus the equation of motion that describes the linear evolution of the perturbation amplitude is [10][11][12][13][14][31][32][33] …”

“…We will assume, as usual, that the velocity field can be approximated by the one corresponding to an ideal inviscid fluid [10][11][12][13][14]31,32]. Then v x± =ξ (t)e ∓ky cos kx,η ± = v y± =ξ (t)e ∓ky sin kx,…”

Dynamic stabilization of Rayleigh-Taylor instability: Experiments with Newtonian fluids as surrogates for ablation fronts

“…[13][14][15]19 These analogies are of great relevance because dynamic stabilization has been already demonstrated experimentally, although a detailed comparison to validate the theory in relation with applications to ICF has not been performed so far. [20][21][22] In this work, we first present the theoretical model for the dynamic stabilization of RTI in Newtonian fluids developed in Ref. 19.…”