The Influence of Strain on Shock-Induced Turbulent Mixing

Abstract

Hydrodynamic instabilities, such as the Rayleigh-Taylor (RTI) and Richtmyer-Meshkov instability (RMI), are responsible for the generation of turbulent mixing layers between fluids separated by an interface. The ability to quantitatively describe and predict these mixing layers is vital for the development of inertial confinement fusion and supersonic combustion, and will improve the understanding of mixing within supernova. Obtaining experimental data for these configurations can be difficult, driving the necessity for accurate simulations and models to capture the flow physics.

The analysis of these instabilities has previously been focused largely towards the planar, Cartesian regime. However, in inertial confinement fusion and supernova collapse the configuration is spherical, which alters the development of the mixing layer. The movement of mixing layers due to a radial velocity causes the mixing layer to be affected by strain rates, which for a spherically symmetric flow can be separated into the radial and circumferential directions. Previously, simulations in spherical geometry have not focused on the effects of these strain rates on the mixing layer development, meaning the effect of the strain rate on the turbulent mixing layer is not well understood.

The influence of the strain rates on RMI and the RMI-induced mixing layer is investigated by applying spatially uniform strain rates in planar geometry and simulating the flow with high-order numerical methods. By advecting the mesh and boundaries in a Lagrangian method with the strain, the uniform velocity gradients can be preserved in the domain. The planar application of the strain rates allows for a decoupling between the strain rates, which is hard to achieve in spherical geometry. The radial strain rate is represented by the axial strain rate (normal to the interface), and the circumferential is represented by the transverse strain rate (in the plane of the interface).