Spatiotemporal perspective on the decay of turbulence in wall-bounded flows

TL;DR

This paper models the decay of turbulence in wall-bounded flows as a nucleation process akin to phase transitions, emphasizing the importance of spatial dynamics over traditional temporal chaos interpretations.

Contribution

It introduces a reduced spatiotemporal model that explains turbulence decay as a nucleation phenomenon, challenging existing chaos-based theories.

Findings

Turbulence decay can be viewed as a nucleation process similar to phase transitions.

An abrupt transition from turbulence to laminar flow occurs at a critical Reynolds number.

Spatial domain analysis reveals a sharp change in flow states independent of chaos lifetime divergence.

Abstract

Using a reduced model focusing on the in-plane dependence of plane Couette flow, it is shown that the turbulent-to-laminar relaxation process can be understood as a nucleation problem similar to that occurring at a thermodynamic first-order phase transition. The approach, apt to deal with the large extension of the system considered, challenges the current interpretation in terms of chaotic transients typical of temporal chaos. The study of the distribution of the sizes of laminar domains embedded in turbulent flow proves that an abrupt transition from sustained spatiotemporal chaos to laminar flow can take place at some given value of the Reynolds number R_{low}, whether or not the local chaos lifetime, as envisioned within low-dimensional dynamical systems theory, diverges at finite R beyond R_{low}.