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Accurately identifying the onset of transitional and turbulent flow within any pipe flow environment is of great interest. Most often, the critical Reynolds number (Re) is used to pinpoint the onset of turbulence. However, the critical Re is known to be highly variable, depending on the specifics of the flow system. Thus, for flows (e.g., blood flows), where only one realization (i.e., one mean Re) exists, the presence of transitional and turbulent flow behaviors cannot be accurately determined. In this work, we aim to address this by evaluating the extent to which instantaneous time-frequency (TF)-based analysis of the fluctuating velocity field can be used to evaluate the onset of transitional and turbulent flow regimes. Because current TF analysis methods are not suitable for this, we propose a novel “wavelet-Hilbert time-frequency” (WHTF) method, which we validate herein. Using the WHTF method, we analyzed the instantaneous dominant frequency of three planar particle image velocimetry-captured pipe flows, which included one steady and two pulsatile with Womersley numbers of 4 and 12. For each case, data were captured at Re's spanning 800–4500. The instantaneous dominant frequency analysis of these flows revealed that the magnitude, size, and coherence of two-dimensional spatial frequency structures were uniquely different across flow regimes. Specifically, the transitional regime maintained the most coherent, but lowest magnitude frequency structures, while the laminar regime had the highest magnitude, lowest coherence, and smallest frequency structures. Overall, this study demonstrates the efficacy of TF-based metrics for characterizing the progression of transition and turbulent flow development.
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Bistability of the large-scale dynamics in quasi-two-dimensional turbulence
In many geophysical and astrophysical flows, suppression of fluctuations along one direction of the flow drives a quasi-two-dimensional upscale flux of kinetic energy, leading to the formation of strong vortex condensates at the largest scales. Recent studies have shown that the transition towards this condensate state is hysteretic, giving rise to a limited bistable range in which both the condensate state as well as the regular three-dimensional state can exist at the same parameter values. In this work, we use direct numerical simulations of thin-layer flow to investigate whether this bistable range survives as the domain size and turbulence intensity are increased. By studying the time scales at which rare transitions occur from one state into the other, we find that the bistable range grows as the box size and/or Reynolds number $Re$ are increased, showing that the bistability is neither a finite-size nor a finite- $Re$ effect. We furthermore predict a cross-over from a bimodal regime at low box size, low $Re$ to a regime of pure hysteresis at high box size, high $Re$ , in which any transition from one state to the other is prohibited at any finite time scale.
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- Award ID(s):
- 2009563
- PAR ID:
- 10341004
- Date Published:
- Journal Name:
- Journal of Fluid Mechanics
- Volume:
- 939
- ISSN:
- 0022-1120
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.209
