Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

McMullen, Ryan Michael; Gallis, Michael A.

doi:10.1103/physreve.110.045104

Title: Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

Journal Article · 06 October 2024 · Physical Review. E

DOI: https://doi.org/10.1103/physreve.110.045104 · OSTI ID:2472760

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Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Here, we investigate hydrodynamic fluctuations in the flow past a circular cylinder near the critical Reynolds number Re_c for the onset of vortex shedding. Starting from the fluctuating Navier-Stokes equations, we perform a perturbation expansion around Re_c to derive analytical expressions for the statistics of the fluctuating lift force. Molecular-level simulations using the direct simulation Monte Carlo method support the theoretical predictions of the lift power spectrum and amplitude distribution. Notably, we have been able to collect sufficient statistics at distances Re ⁡/ Re_c – 1 = O ⁡(10^–3) from the instability that confirm the appearance of non-Gaussian fluctuations, and we observe that they are associated with intermittent vortex shedding. These results emphasize how unavoidable thermal-noise-induced fluctuations become dramatically amplified in the vicinity of oscillatory flow instabilities and that their onset is fundamentally stochastic.

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Research Organization:: Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE National Nuclear Security Administration (NNSA), Office of Defense Programs (DP)

Grant/Contract Number:: NA0003525

OSTI ID:: 2472760

Report Number(s):: SAND--2024-13841J

Journal Information:: Physical Review. E, Journal Name: Physical Review. E Journal Issue: 4 Vol. 110; ISSN 2470-0045

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

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Title: Hydrodynamic fluctuations near a Hopf bifurcation: Stochastic onset of vortex shedding behind a circular cylinder

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