Simulations and models to describe initial condition effects on the multi-mode Richtmyer-Meshkov instability

The Richtmyer-Meshkov instability (RMI) is shock driven and affects many phenomena from inertial confinement fusion to supernova explosions. The behavior of single-modes in the RMI has been studied expensively but less is known with broadband perturbations that occur in applications. Here, we describe extensive numerical simulations and modeling of the RMI with broadband perturbations with a wavenumber (k) power spectrum of the form P ∝ k^m. The bubble amplitude h_B is found to grow in two stages. First, there is secular growth in time at a rate consistent with linear theory. Second, when h_B becomes comparable to the average wavelength 2π/〈k〉 of the spectrum, it grows as a power law in time h_B ~ t^θ. This behavior is described and modeled over a wide range of m, spectral width, initial amplitudes and time.