Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

TL;DR

This paper investigates the universal statistical properties of driven symmetric binary fluid mixtures in a nonequilibrium steady state, revealing continuous variation of scaling exponents and amplitude ratios with crosscorrelations, and clarifying the scaling behavior of structure functions.

Contribution

The study establishes the form of structure functions based on symmetries and shows how exponents and ratios vary with crosscorrelations in binary fluid turbulence.

Findings

Scaling exponents and amplitude ratios vary continuously with crosscorrelations.

Conventional structure functions exhibit simple scaling even in weak concentration limits.

Universal properties are elucidated through symmetry analysis and are experimentally verifiable.

Abstract

We elucidate the universal properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid mixture, an example of active advection, in its miscible phase. We use the symmetries of the equations of motion to establish the appropriate form of the structure functions which characterise the statistical properties of the NESS of a driven symmetric binary fluid mixture. We elucidate the universal properties described by the scaling exponents and the amplitude ratios. Our results suggest that these exponents and amplitude ratios vary continuously with the degree of crosscorrelations between the velocity and the gradient of the concentration fields. Furthermore, we demonstrate, in agreement with Celani et al, Phys. Rev. Lett., 89, 234502 (2002, that the conventional structure functions as used in passive scalar turbulence studies exhibit only simple scaling in the problem of symmetric binary fluid mixture even in the weak concentration limit. We also discuss possible experimental verifications of our results.