Scaling evolution in shock-induced transition to turbulence

In this experimental study, a column of heavy gas (SF6) surrounded by light gas (air) is accelerated by a planar Mach 1.2 shock. Richtmyer-Meshkov instability on the initially diffuse air-SF6 interface determines the repeatable large-scale vortex dynamics of the system after the shock passage. Subsequently secondary instabilities form, with the system eventually transitioning to turbulence. We present highly resolved measurements of two components of the instantaneous velocity fields. With these measurements, we investigate the evolution of velocity statistics over a substantial range of scales in terms of structure functions. The latter evolve to exhibit late-time behavior consistent with the Kolmogorov scaling law for fully developed turbulence, despite the transitional character, anisotropy, and inhomogeneity of our flow. Ensemble averaging and comparison with instantaneous results reveal a trend towards the same scaling manifested much earlier by the structure functions of the fluctuating velocity components.