Kovasznay modes in stability of self-similar ablation flows of ICF

The history of the linear perturbations in a 'laser imprinting' configuration in inertial confinement fusion (ICF) is described. The time-dependent mean flow is provided by a self-similar solution of gas dynamics equations with nonlinear heat conduction for semi-infinite slabs of perfect gases. The analysis is conducted with the Kovasznay modes, namely the vorticity, acoustic and entropy modes. Exact propagation equations for these three basic modes are derived. Both the similarity solutions and their linear perturbations are numerically computed with an adaptive multi-domain Chebyshev method. In particular, the dynamics of the shock wave is detailed. The shock wave response, for all quantities (vorticity, pressure, entropy,...) consists in several bursts with peak amplitude decreasing exponentially with time. The occurrence of such 're-growths' implies that, past the first decay of shock-front oscillations, an amplified level of perturbations may be expected to persist over a finite duration and for a finite bandwidth. This perturbation amplification could enhance the seeding of the ablative Rayleigh-Taylor instability growth during an ICF pellet implosion acceleration stage