A statistical mechanics framework for the large-scale structure of turbulent von K{\'a}rm{\'a}n flows

TL;DR

This paper applies a statistical mechanics approach to analyze large-scale coherent steady states in turbulent von Kármán flows, drawing analogies with ferromagnetism to understand their stability and symmetry properties.

Contribution

It introduces a lattice model framework to describe von Kármán flow states and interprets their stability and symmetry breaking phenomena through a ferro-magnetism analogy.

Findings

Coherent steady states can be modeled as equilibrium states of lattice models.

The stability and symmetry breaking of these states are analogous to ferromagnetic systems.

The framework provides a new perspective on large-scale turbulence structures.

Abstract

In the present paper, recent experimental results on large scale coherent steady states observed in experimental von K{\'a}rm{\'a}n flows are revisited from a statistical mechanics perspective. The latter is rooted on two levels of description. We first argue that the coherent steady states may be described as the equilibrium states of well-chosen lattice models, that can be used to define global properties of von K{\'a}rm{\'a}n flows, such as their temperatures. The equilibrium description is then enlarged, in order to reinterpret a series of results about the stability of those steady states, their susceptibility to symmetry breaking, in the light of a deep analogy with the statistical theory of Ferromagnetism. We call this analogy "Ferro-Turbulence"