Stochastic micromodel of the Couette flow

TL;DR

This paper introduces a stochastic micromodel for Couette flow using a Markov exclusion process, demonstrating phase transitions between laminar and turbulent profiles and capturing key features of viscous liquids.

Contribution

It presents a novel stochastic particle system model for Couette flow that exhibits phase transitions, bridging microscopic interactions and macroscopic flow behavior.

Findings

Mean velocity profile matches incompressible viscous liquid behavior

Existence of phase transition between laminar and turbulent flow profiles

Model captures local interactions and velocity exchanges in the flow

Abstract

We study Markov exclusion process for a particle system with a local interaction in the integer strip. This process models the exchange of velocities and particle-hole exchange of the liquid molecules. It is shown that the mean velocity profile corresponds to the behaviour which is characteristic for incompressible viscous liquid. We prove the existence of phase transition between laminar and turbulent profiles.