Modeling transitional plane Couette flow

TL;DR

This paper develops a reduced-order model of plane Couette flow using Galerkin methods, capturing its sub-critical transition and turbulent transient statistics, aligning well with experimental observations.

Contribution

It introduces a PDE-based model derived via Galerkin method that accurately reproduces key flow behaviors and transient statistics of plane Couette flow.

Findings

Model reproduces sub-critical transition behavior.

Simulates turbulent transients matching experimental data.

Captures space-time dependence of flow modes.

Abstract

The Galerkin method is used to derive a realistic model of plane Couette flow in terms of partial differential equations governing the space-time dependence of the amplitude of a few cross-stream modes. Numerical simulations show that it reproduces the globally sub-critical behavior typical of this flow. In particular, the statistics of turbulent transients at decay from turbulent to laminar flow displays striking similarities with experimental findings.