Shock Front Distortion and Richtmyer-Meshkov-like Growth Caused by a Small Pre-Shock Non-Uniformity; Journal article

摘要

Response of a shock front to small pre-shock non-uniformities of density, pressure and velocity is studied theoretically and numerically. These pre-shock nonuniformities emulate imperfections of a laser target, due either to its manufacturing, like joints or feeding tubes, or to pre-shock perturbation seeding/growth, as well as density fluctuations in foam targets, 'thermal layers' near heated surfaces, etc. Similarly to the shock-wave interaction with a small non-uniformity localized at a material interface which triggers a classical Richtmyer-Meshkov (RM) instability, interaction of a shock wave with periodic or localized pre-shock perturbations distributed in the volume distorts the shape of the shock front and can cause a RM-type instability growth. Explicit asymptotic formulae describing distortion of the shock front and the rate of RM-type growth are presented. These formulae are favorably compared both to the exact solutions of the corresponding initial- boundary-value problem and to numerical simulations. It is demonstrated that a small density modulation localized sufficiently close to a flat target surface produces the same perturbation growth as an 'equivalent' ripple on the surface of a uniform target, characterized by the same initial areal mass modulation amplitude.