Critical properties of laminar-turbulent pattern emergence in plane Couette flow

¹ LadHyX, Institut Polytechnique de Paris, École polytechnique - Palaiseau, 91120, France
² Graduate School of Engineering Science, Osaka University - Toyonaka 560-0043, Japan

Received: 27 March 2025
Accepted: 30 July 2025

Abstract

When decaying to laminar flow from uniform turbulence at decreasing Reynolds number R, wall-bounded flows often display a complex regime made of coexisting laminar and turbulent domains in a range . The ultimate decay at R_g is well understood as a directed percolation (DP) process representative of a non-equilibrium universality class. The status of the pattern's emergence at R_t is much less clear-cut. Here, we study this problem in the emblematic case of flow between counter-translating parallel plates, plane Couette flow. Through numerical simulations in an extended domain, we demonstrate that this phenomenon exhibits characteristics consistent with a second-order phase transition. Ginzburg-Landau–like envelopes derived from turbulence modulations serve to define order parameters. The variance of their temporal fluctuations (conjugate susceptibilities in the phase transition context) and the coherence lengths extracted from their spatial autocorrelations show diverging trends as the threshold is approached. The exponents corresponding to these divergences, and , appear significantly different from the classical values and , signalling unconventional critical properties. We discuss the possibility that these findings could be archetypal of an original out-of-equilibrium universality class at R_t, like the DP universality class observed at R_g.