A cascade model for the discontinuous absorbing phase transition between turbulent and laminar flows

TL;DR

This paper presents a minimal statistical physics model capturing the discontinuous transition between laminar and turbulent flows, reproducing key features like metastability and turbulence lifetime increase.

Contribution

It introduces a simple energy transfer model that qualitatively reproduces the subcritical laminar-turbulent transition and aligns with Kolmogorov turbulence phenomenology.

Findings

Model reproduces discontinuous transition features

Turbulence lifetime increases faster-than-exponentially with Reynolds number

Model aligns with Kolmogorov K41 turbulence theory

Abstract

We introduce a minimal model of energy transfer through scales to describe, at a qualitative level, the subcritical transition between laminar and turbulent flows, viewed in a statistical physics framework as a discontinuous absorbing phase transition. The main control parameter of the model is a Reynolds number that compares energy transfer to viscous dissipation on a large length scale. In spite of its simplicity, the model qualitatively reproduces a number of salient features of the subcritical laminar-turbulent transition, including the existence of an absorbing laminar state, the discontinuous onset of a metastable fluctuating turbulent state above a threshold Reynolds number, and a faster-than-exponential increase of the turbulence lifetime when increasing the Reynolds number. The behavior of the model is also consistent, at high Reynolds number, with the Kolmogorov K41 phenomenology of fully developed turbulence.