Energy transfer in simple and active binary fluid turbulence {\bf {-}} a false friend of incompressible MHD turbulence

TL;DR

This paper derives exact relations for energy transfer in binary fluid turbulence, highlighting differences from MHD turbulence and proposing a new energy spectrum law influenced by activity parameters.

Contribution

It introduces novel exact relations for binary fluid turbulence and explores conditions leading to inverse energy cascades, differing from incompressible MHD turbulence.

Findings

Exact relations for energy transfer are derived for binary fluid turbulence.

Inverse energy cascade is possible depending on activity parameters.

A $k^{-3/2}$ energy spectrum law is predicted.

Abstract

Inertial range energy transfer in three dimensional fully developed binary fluid turbulence is studied under the assumption of statistical homogeneity. Using two point statistics, exact relations corresponding to the energy cascade are derived (i) in terms of two-point increments and (ii) two-point correlators. Despite having some apparent resemblances, the exact relation in binary fluid turbulence is found to be different from that of the incompressible MHD turbulence (Politano and Pouquet, GRL, 1998). Besides the usual direct cascade of energy, under certain situations, an inverse cascade of energy is also speculated depending upon the strength of the activity parameter and the interplay between the two-point increments of the fluid velocity and the composition gradient fields. An alternative form of the exact relation is also derived in terms of the `upsilon' variables and a subsequent phenomenology is also proposed predicting a $k^{-{3}/{2}}$ law for the turbulent energy spectrum.