The Onset of Metastable Turbulence in Pipe Flow
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866908398468988928 |
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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 |
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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 |