Dynamical Stabilization of Shockwave-driven Material Interfaces via Machine Learning: Annihilation of Vortical Flow for the Taming of Richtmyer-Meshkov Instability

The interaction of shockwaves at material interfaces of differing impedance results in an inherently unstable dynamical trajectory, with non-linear growth of perturbations and subsequent jetting occurring in chaotic fashion owing to the well-known Richtmyer-Meshkov instability (RMI). There are very few known solutions to preventing the formation of RMI and even partial progress toward its stabilization would enable many important applications, such as more effective mining and energy exploration, aerospace engineering and inertial confinement fusion. Beginning with Onsager (“Statistical Hydrodynamics”, 1949), and further developed through more modern treatments, the field dynamics that generate and sustain this instability have been mathematically described in an equivalent form whereby a symplectic, Hamiltonian system of N point vortices can interact and evolve through equation of motion. In this alternate picture, the time propagation of the field (and the baroclinic forces that generate instability) is projected into a reduced order form with vortex evolution as the key quantity of interest, but at the expense of non-linear complexity. Through application of new machine learning workflows, coupled to simulated hydrodynamics, we show that there exist solutions to the problem of RMI in which the vortices at the interface can be destroyed, a concept that we denote as the Annihilation of Vortical Flow (AVF). The engineered solutions, found via ML hydrodynamic design optimization, are generated via special drive conditions that have been manufactured with modern additive techniques. While the supercomputing resources necessary to apply hydrodynamic design optimization are massive, it has been found that the solution space for stabilization of RMI is surprisingly large.