Universal relaxation of turbulent binary fluids

TL;DR

This paper investigates the universal relaxation process of turbulent binary fluids using direct numerical simulations, revealing distinct relaxation pathways for the bulk and interface, and proposing a universal pathway based on vanishing nonlinear transfer.

Contribution

It introduces the first systematic numerical study of turbulent relaxation in binary fluids and proposes a universal relaxation pathway based on the suppression of turbulent cascades.

Findings

Bulk and interface relaxations differ in binary fluids.

A universal relaxation pathway is proposed based on vanishing nonlinear transfer.

Interface relaxation follows a Helmholtz-like pressure balance.

Abstract

Upon quenching the forcing, a turbulent system tends to attain the state of stable equilibrium through the process of turbulent relaxation. Such relaxation in binary fluids is of surmount interest for both fundamental science understanding and industrial applications. A systematic investigation of the same has been carried out, for the first time, using direct numerical simulations of Cahn-Hilliard-Navier-Stokes equations. With the help of a thorough scanning, the bulk of each fluid and its interface are found to relax in a different way. However, using the principle of vanishing nonlinear transfer, we propose a convincing, universal pathway of obtaining the turbulent relaxed states for both the bulk and the interface which attain a relaxed state when the turbulent cascades of the inviscid invariants are suppressed. Interestingly, the relaxation of the bulk turns up to be subtly different from the turbulent relaxation of a single hydrodynamic fluid and the interface relaxation is found to follow a Helmholtz-like pressure-balanced condition.