Universality of scaling and multiscaling in turbulent symmetric binary fluids

Abstract

We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions (3d). We show, for the first time, via Direct Numerical Simulations (DNS) that structure functions of the velocity and the concentration gradient exhibit multiscaling in 3d and extended self-similarity (ESS). We also find that, in contrast to the well-known passive scalar turbulence problem, structure functions of the concentration show simple scaling. We propose a new shell model for SBF turbulence which preserve all the invariances in the ideal limit of the SBF equations and which reduces to a well-known shell model for fluid turbulence in the zero concentration field limit. We show that the shell model has the same scaling properties as the 3d SBF equations. Our combined results from our DNS of the SBF equations and shell-model studies consistently bring out the multiscaling of the velocity and concentration gradient fields and simple scaling of the concentration field.