Nonlinear dynamics of double-layer unstable interfaces with non-uniform velocity shear

Abstract

The interaction of double-layer density stratified interfaces with initial non-uniform velocity shear is investigated theoretically and numerically, taking the incompressible Richtmyer–Meshkov instability as an example. The linear analysis for providing the initial conditions in numerical calculations is performed, and some numerical examples of vortex double layers are presented using the vortex sheet model. We show that the density stratifications (Atwood numbers), the initial distance between two interfaces, and the distribution of the initial velocity shear determine the evolution of vortex double layers. When the Atwood numbers are large, the deformation of interfaces is small, and the distance between the two interfaces is almost unchanged. On the other hand, when the Atwood numbers are small and the initial distance between two interfaces is sufficiently close (less than or equal to the half of the wavelength of the initial disturbance), the two interfaces get closer to each other and merge at the last computed stage due to the incompressibility. We confirm this theoretically expected fact numerically.