Work

Stability of N‐front and N‐back solutions in the Barkley model

Year: 2025

Type: article

Abstract: ABSTRACT In this article, we establish for an intermediate Reynolds number domain the stability of ‐front and ‐back solutions for each corresponding to traveling waves, in an experimentally validated model for the transition to turbulence in pipe flow proposed in [Barkley et al., Nature 526(7574):550‐553, 2015]. We base our work on the existence analysis of a heteroclinic loop between a turbulent and a laminar equilibrium proved by Engel, Kuehn and de Rijk in Engel, Kuehn, de Rijk, Nonlinearity 35:5903, 2022, as well as some results from this work. The stability proof follows the verification of a set of abstract stability hypotheses stated by Sandstede in [SIAM Journal on Mathematical Analysis 29.1 (1998), pp. 183‐207] for traveling waves motivated by the FitzHugh–Nagumo equations. In particular, this completes the first detailed analysis of Engel, Kuehn and de Rijk in [Engel, Kuehn, de Rijk, Nonlinearity 35:5903, 2022] leading to a complete existence and stability statement that nicely fits within the abstract framework of waves generated by twisted heteroclinic loops.

Source: GAMM-Mitteilungen

DOI: 10.1002/gamm.70001

Authors: Christian Kuehn, Pascal Sedlmeier

Institution: Technical University of Munich

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,140

Funders: Massachusetts Department of Fish and Game, Volkswagen Foundation