Saddle-node bifurcation during the relaminarization of turbulent puffs in pipe

TL;DR

This paper investigates the final stage of turbulent puff relaminarization in pipes, revealing a saddle-node bifurcation characterized by a universal square-root scaling law, modeled using the Riccati equation.

Contribution

It uncovers the saddle-node bifurcation mechanism in pipe flow relaminarization and proposes a simple Riccati equation model for these bifurcations.

Findings

Identification of saddle-node bifurcation in relaminarization

Universal square-root scaling law observed

Riccati equation effectively models the bifurcation process

Abstract

Turbulent puffs in a pipe persist for a long time before abruptly transitioning to laminar flow through viscous exponential decay. Direct numerical simulation results reveal a saddle-node bifurcation sequence governing the final relaminarization stage. Specifically, a universal square-root scaling law in the annihilation of critical points that is indicative of a saddle-node bifurcation. The Riccati equation has been proposed as a straightforward approach to modeling these bifurcations.