Emergence of spatio-temporal dynamics from exact coherent solutions in pipe flow

TL;DR

This paper demonstrates how invariant solutions of the Navier-Stokes equations lead to the emergence of complex spatio-temporal patterns in pipe flow, providing a dynamical-system explanation for turbulent-laminar patterns.

Contribution

It introduces a dynamical-system framework showing how merging chaotic spots produce observed turbulent-laminar patterns in pipe flow.

Findings

Chaotic spots with different properties merge in phase space.

Merged spots lead to complex spatio-temporal patterns.

Provides a foundation for understanding turbulence patterns in shear flows.

Abstract

Turbulent-laminar patterns are ubiquitous near transition in wall-bounded shear flows. Despite recent progress in describing their dynamics in analogy to non-equilibrium phase transitions, there is no theory explaining their emergence. Dynamical-system approaches suggest that invariant solutions to the Navier--Stokes equations, such as traveling waves and relative periodic orbits in pipe flow, act as building blocks of the disordered dynamics. While recent studies have shown how transient chaos arises from such solutions, the ensuing dynamics lacks the strong fluctuations in size, shape and speed of the turbulent spots observed in experiments. We here show that chaotic spots with distinct dynamical and kinematic properties merge in phase space and give rise to the enhanced spatio-temporal patterns observed in pipe flow. This paves the way for a dynamical-system foundation to the phenomenology of turbulent-laminar patterns in wall-bounded extended shear flows.