The Onset of Metastable Turbulence in Pipe Flow

Fuente: arXiv
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Main Authors: Guan, Jiashun, Tao, Jianjun
Format: Preprint
Published: 2025
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author Guan, Jiashun
Tao, Jianjun
author_facet Guan, Jiashun
Tao, Jianjun
contents The onset of turbulence in pipe flow has been a fundamental challenge in physics, applied mathematics, and engineering for over 140 years. To date, the precursor of this laminar-turbulent transition is recognized as transient turbulent spots or puffs, but their defining characteristics - longevity, abrupt relaminarization, and super-exponential lifetime scaling - have been lack of first-principles explanations. By combining extensive computer simulations, theory, and verifications with experimental data, we identify distinct puff relaminarizations separated by a critical Reynolds number, which are defined by a noisy saddle-node bifurcation derived from the Navier-Stokes equations. Below the critical number, the mean lifetime of puff follows a square-root scaling law, representing an intrinsically deterministic decay dominated by the critical slowing down. Above the critical value, the bifurcation's node branch creates a potential well stabilizing the turbulence, while the saddle branch mediates stochastic barrier-crossing events that drive memoryless decay - a hallmark of metastable states. Accordingly, the mean lifetimes are solved theoretically and can be fitted super-exponentially. By quantifying the deterministic and stochastic components in the kinetic energy equation, the lifetime statistics of puff are analyzed in a unified framework across low-to-moderate Reynolds number regimes, uncovering the mechanisms governing the transition to metastable turbulence in pipe flows.
format Preprint
id arxiv_https___arxiv_org_abs_2504_14465
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The Onset of Metastable Turbulence in Pipe Flow
Guan, Jiashun
Tao, Jianjun
Fluid Dynamics
Chaotic Dynamics
Pattern Formation and Solitons
The onset of turbulence in pipe flow has been a fundamental challenge in physics, applied mathematics, and engineering for over 140 years. To date, the precursor of this laminar-turbulent transition is recognized as transient turbulent spots or puffs, but their defining characteristics - longevity, abrupt relaminarization, and super-exponential lifetime scaling - have been lack of first-principles explanations. By combining extensive computer simulations, theory, and verifications with experimental data, we identify distinct puff relaminarizations separated by a critical Reynolds number, which are defined by a noisy saddle-node bifurcation derived from the Navier-Stokes equations. Below the critical number, the mean lifetime of puff follows a square-root scaling law, representing an intrinsically deterministic decay dominated by the critical slowing down. Above the critical value, the bifurcation's node branch creates a potential well stabilizing the turbulence, while the saddle branch mediates stochastic barrier-crossing events that drive memoryless decay - a hallmark of metastable states. Accordingly, the mean lifetimes are solved theoretically and can be fitted super-exponentially. By quantifying the deterministic and stochastic components in the kinetic energy equation, the lifetime statistics of puff are analyzed in a unified framework across low-to-moderate Reynolds number regimes, uncovering the mechanisms governing the transition to metastable turbulence in pipe flows.
title The Onset of Metastable Turbulence in Pipe Flow
topic Fluid Dynamics
Chaotic Dynamics
Pattern Formation and Solitons
url https://arxiv.org/abs/2504.14465