Analysis of dynamics, stability and flow fields’ structure of an accelerated hydrodynamic discontinuity with interfacial mass flux by a general matrix method

We develop a general matrix method to analyze from a far field the dynamics of an accelerated interface between incompressible ideal fluids of different densities with interfacial mass flux and negligible stratification. We solve the linearized boundary value problem for the dynamics conserving mass, momentum and energy in the bulk and at the interface. We find a hydrodynamic instability that develops only when the acceleration magnitude exceeds a threshold. This critical threshold value depends on the magnitudes of the steady velocities of the fluids, the ratio of their densities, and the wavelength of the initial perturbation. The flow has potential velocity fields in the fluid bulk and is shear-free at the interface. The quantitative, qualitative and formal properties of the accelerated conservative dynamics depart from those of accelerated Landau-Darrieus and Rayleigh-Taylor dynamics. New diagnostic benchmarks are identified for experiments and simulations of unstable interfaces.