Non-reciprocal Binary-fluid Turbulence

TL;DR

This paper introduces a novel non-reciprocal binary-fluid turbulence model, revealing unique inverse cascade behavior and non-reciprocal flux properties, expanding understanding of turbulence influenced by non-reciprocal interactions.

Contribution

The study develops a 2D Non-Reciprocal Cahn-Hilliard-Navier-Stokes model to explore turbulence with non-reciprocal interactions, uncovering new turbulence phenomena and flux suppression effects.

Findings

Discovery of inverse energy cascade with spectrum ~k^{-5/3}

Identification of non-reciprocal flux J in turbulence

Suppression of flux J as Reynolds number increases

Abstract

Although effective non-reciprocal interactions have been investigated in a variety of fields, their consequences have not been explored in hydrodynamical turbulence. We initiate such an exploration by introducing non-reciprocal binary-fluid tubulence and uncover its properties by developing a two-dimensional (2D) Non-Reciprocal Cahn-Hilliard-Navier-Stokes (NRCHNS) model. We show that, as we increase the strength of the non-reciprocal terms, this model displays a hitherto unanticipated type of turbulence, with an inverse cascade of energy and an energy spectrum $E(k)\sim k^{-5/3}$, reminiscent of the well-known inverse cascade in forced, 2D fluid turbulence, but distinct from it, in so far as it develops a non-reciprocal flux $\mathbf J$. We demonstrate how NRCHNS turbulence suppresses $J(t) = |\mathbf J|$, as the Reynolds number increases. We compare and contrast 2D NRCHNS turbulence with its fluid-turbulence counterpart by examining spectra, fluxes, spectral balances, flow topologies, and signatures of multifractality.