Nonlinear growth of the shock-accelerated instability of a thin fluid layer

Richtmyer-Meshkov instability causes spatially periodic perturbations initially imposed on a shock-accelerated, thin gas layer to develop into one of three distinct flow patterns. Planar laser-induced fluorescence imaging of the evolving layer, produced by a perturbed SF₆ planar jet in air, shows an apparent flow bifurcation that is observed as mushroom-shaped or sinuous-shaped interfacial patterns. Analysis of this nonlinear instability growth, accomplished by modelling the flow field as a row of line vortices, predicts that the layer thickness grows logarithmically at later times and compares well with our measurements. Because the row of vortices is unstable, the model also provides an explanation for the appearance of the three observed interfacial patterns.