A unified theoretical model for spatiotemporal development of Rayleigh–Taylor and Richtmyer–Meshkov fingers

An initially perturbed interface between two fluids of different densities is usually unstable when driven by an acceleration or a shock wave; it known as Rayleigh–Taylor instability Richtmyer–Meshkov instability. One the most significant issues in these instabilities spatiotemporal development fingers generated at interface, which plays important role both scientific research (e.g. supernova explosion) and engineering applications inertial confinement fusion). Accurate theoretical solution interfacial remains unsolved challenging problem since Taylor's seminal work more than seven decades ago. This paper reports unified theory established for such phenomena combining classical potential-flow dual-source model to address long-standing difficulty highlighted initial-value sensitivity strong nonlinearity. It first time accurately predict long-time developments growth rate shape curvature all density ratios three dimensions. Moreover, new clearly reveals nonlinear coupling mechanism evolution, especially explains origin overshot curve.