Fractal characteristics of interfaces in Richtmyer–Meshkov turbulence

Abstract

This work investigates the fractal dimension of the spike front and the bubble front in Richtmyer–Meshkov (RM) turbulence with initial broadband and narrowband perturbations. The fractal dimension $D_f$ of interfaces is found to be intimately associated with interfacial mixing, exhibiting a gradual increase with interface evolution until it attains a stable value, between $D_f\approx 2.2\sim 2.33$, upon entering the self-similar stage. The fractal dimension on the spike front is closer to the universal fractal dimension of fully-developed turbulence, indicating stronger turbulent fluctuations there. Large-scale perturbations render the interfaces more two-dimensional thereby resulting in a lower fractal dimension. The results demonstrate that the fractal dimension, $D_{f3}$, of a surface in three dimensions can be faithfully reflected by the fractal dimension, $D_{f2}$, of the interface of its two-dimensional projection. This finding validates the additive rule of $D_{f3}=D_{f2}+1$ in RM turbulence, which is of considerable utility for experimental research. The filtering approach is furthermore employed to illustrate the scale-invariance of the fractal interfaces. The fractal features of the early spike and bubble interfaces can be described by a simple model fractal of the Koch curve, with distinct scale factors.