Universality of scaling and multiscaling in turbulent symmetric binary fluids

Abstract

We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions. We show, via direct numerical simulations (DNSs) that structure functions of the velocity and the concentration gradient exhibit multiscaling in three dimensions (3D) and extended self-similarity. 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 shell model for SBF turbulence that preserves all the invariances in the ideal limit of the SBF equations and 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 three-dimensional SBF equations. Our combined results from our DNSs 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.