Wavelength selection in shock-induced Kelvin-Helmholtz instability*

We conducted experimental shock-tube studies of a tilted, shock-accelerated heavy gas cylinder where we observed perturbation growth on the upstream and downstream density interfaces initially bounding the heavy gas in the nominal plane of symmetry of the flow. The dominant perturbation wavelength away from the shock-tube wall was highly repeatable for the same initial conditions, and varied with the column tilt angle and Mach number. We proposed a simple geometrically-based explanation for the wavelength selection mechanism, using two-dimensional considerations. Recently conducted numerical simulations of tilted and shock-accelerated gas curtains (two-dimensional) and cylinders (three-dimensional) suggest that the same physics are indeed responsible for interfacial perturbation growth in both the two- and three-dimensional formulation: baroclinic vorticity deposition on the leading and trailing edge of the curtain (cylinder) produces shear layers, leading to shock-driven Kelvin-Helmholtz instability (SDKHI). The dominant perturbation wavelength can be similarly explained by the geometric parameters of the shock-compressed curtain or cylinder. Additional examination of experimental and numerical data also reveals a second SDKHI wavelength near one of the walls of the shock tube due to reflected shock interacting with the solid boundary.