Work

Slow-fast dynamics in the localized turbulent pipe flow with transitional Reynolds number

Year: 2026

Type: article

Abstract: This paper explores the slow-fast dynamics in localized turbulence for an experimentally validated model (Barkley et al. (Nature, 2015)), which describes the onset of turbulent pipe flow through a reaction-diffusion system. By geometric singular perturbation theory and the generalized rotated vector field method, we demonstrate the existence and wave speed of traveling pulses for transitional Reynolds numbers, which correspond to the homoclinic orbits connecting the unique equilibrium in the slow-fast traveling wave system. Subsequently, we present the spectral stability of traveling pulses based on asymptotic theory and the Evans function. Additionally, we investigate the existence of periodic wave trains corresponding to periodic orbits in the slow-fast traveling wave system. Furthermore, the coexisting geometric structures of periodic and homoclinic orbits can be demonstrated for the transitional Reynolds number.

Source: Communications on Pure &amp Applied Analysis

DOI: 10.3934/cpaa.2026.102935

Authors: Zhengkang Li, Xingbo Liu

Institutions: China University of Mining and Technology, East China Normal University

Language: English

Topic: Nonlinear Dynamics and Pattern Formation

Subfield: Computer Networks and Communications

Field: Computer Science

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Fundamental Research Funds for the Central Universities

Awards: G2629724599, G4025817527, G8175904195