The growth of fractal dimension of an interface evolution from the interaction of a shock wave with a rectangular block of SF6

The interface between air and a rectangular block of sulphur hexafluoride (SF6), impulsively accelerated by the passage of a planar shock wave, undergoes Richtmyer-Meshkov instability and the flow becomes turbulent. The evolution of the interface was previously simulated using a multi-component model based on a thermodynamically consistent and fully conservative formulation and results were validated against available experimental data (Bates et al. Richtmyer-Meshkov instability induced by the interaction of a shock wave with a rectangular block of SF6, Phys Fluids, 2007; 19:036101). In this study, the CFD results are analyzed using the fractal theory approach and the evolution of fractal dimension of the interface during the transition of the flow into fully developed turbulence is measured using the standard box-counting method. It is shown that as the Richtmyer-Meshkov instability on the interface develops and the flow becomes turbulent, the fractal dimension of the interface increases asymptotically toward a value close to 1.39, which agrees well to those measured for classical shear and fully developed turbulences.