Universal relaxation of turbulent binary fluids

Abstract

Turbulent relaxation is the process of turbulent systems reaching the state of equilibrium, starting upon quenching the turbulence forcing acting on them. Such relaxation in binary fluids is instrumental for both fundamental science understanding and industrial applications, although potential differences in the relaxation of bulk and interface are still to be identified. Using direct numerical simulations of Cahn-Hilliard-Navier-Stokes equations, here we show that the bulk and the interface relax towards different states. However, both the relaxation channels can be accounted for via a universal pathway based on the recently proposed principle of vanishing nonlinear transfers. We find that the bulk of each fluid relaxes differently from the turbulent relaxation of a single hydrodynamic fluid. At the same time, the interface relaxes towards a Helmholtz-like pressure-balanced state. The present methodology can be directly applied to predict the turbulent relaxed states in active binary mixtures as well as other complex fluid systems.