# CHNS: A case study of turbulence in elastic media

## TL;DR

This paper reviews recent advances in understanding turbulence in elastic media, specifically focusing on the Cahn-Hilliard Navier-Stokes system, highlighting structure formation, dual cascade interactions, and analogies with magnetohydrodynamics.

## Contribution

It presents new theoretical insights into 2D CHNS turbulence, emphasizing blob formation and flux expulsion phenomena, with comparisons to MHD and elastic media.

## Key findings

- Blob formation influences dual cascade dynamics.
- Concentration gradients respond to eddies similarly to flux expulsion in MHD.
- Elastic media exhibit memory effects constraining turbulence behavior.

## Abstract

Recent progress in the study of Cahn-Hilliard Navier-Stokes (CHNS) turbulence is summarized. This is an example of \textit{elastic turbulence}, which can occur in elastic (i.e. self-restoring) media. Such media exhibit memory due freezing-in laws, as does MHD, which in turn constrains the dynamics. We report new results in the theory of CHNS turbulence in 2D, with special emphasis on the role of structure (i.e. `blob') formation and its interaction with the dual cascade. The evolution of a concentration gradient in response to a single eddy -- analogous to flux expulsion in MHD -- is analyzed. Lessons learned are discussed in the context of MHD and other elastic media.