An official website of the United States government
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.
more »
« less
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.
more »
« less
- 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
More Like this
-
-
The bistable fluttering response of heavy inverted flags with different aspect ratios ( $AR$ ) is investigated to determine how the vortical structures affect the intermittent vibration response of the flag. A heavy inverted flag in a uniform flow may exhibit several response modes; amongst them are three major modes that occur over an extended velocity range: stationary, large-scale periodic oscillation and one-sided deflected modes. Significant hysteretic bistability is observed at the transition between these modes for all $AR$ , which is notably different from the conventional flag vibration with a fixed leading edge and free trailing edge where no hysteresis is observed at the lower $AR$ limit ( $AR<1$ ). The difference is associated with the distinct roles of vortices around the flag. Experiments with flags made of spring steel are conducted in a wind tunnel, where the flow speed is steadily increased and later decreased to obtain different oscillatory modes of the heavy inverted flags. The experimental results are used to validate the numerical model of the same problem. It is found that different critical velocities exist for increasing and decreasing flow velocities, and there is a sustained hysteresis for all $AR$ controlled by the initiation threshold and growth of the leading-edge and side-edge vortices. The effect of the vortices in the bistable oscillation regime is quantified by formulating a modal force partitioning approach. It is shown that $AR$ can significantly alter the static and dynamic vortex interaction with the flexible plate, thereby changing the flag's hysteresis behaviour and bistable response.more » « less
-
Abstract Multi-welled energy landscapes arising in shells with nonzero Gaussian curvature typically fade away as their thickness becomes larger because of the increased bending energy required for inversion. Motivated by this limitation, we propose a strategy to realize doubly curved shells that are bistable for any thickness. We then study the nonlinear dynamic response of one-dimensional (1D) arrays of our universally bistable shells when coupled by compressible fluid cavities. We find that the system supports the propagation of bidirectional transition waves whose characteristics can be tuned by varying both geometric parameters as well as the amount of energy supplied to initiate the waves. However, since our bistable shells have equal energy minima, the distance traveled by such waves is limited by dissipation. To overcome this limitation, we identify a strategy to realize thick bistable shells with tunable energy landscape and show that their strategic placement within the 1D array can extend the propagation distance of the supported bidirectional transition waves.more » « less
-
Recent experiments on multilayer rhombohedral graphene have unearthed a number of interesting phenomena in the regime where integer and fractional quantum anomalous Hall phenomena were previously reported. Specifically, at low temperature (𝑇) and low applied currents, an “extended” integer quantum anomalous Hall (EIQAH) state is seen over a wide range of the phase diagram. As the current is increased, at low 𝑇, the EIQAH state undergoes a phase transition to a metallic state at generic fillings, and to the fractional quantum anomalous Hall (FQAH) state at the Jain fillings. Increasing temperature at the Jain fillings also leads to an evolution out of the EIQAH state to the Jain state. Here we provide an interpretation of many of these observations. We describe the EIQAH state as a crystalline state (either of holes doped into the 𝜈=1 state or an anomalous Hall crystal of electrons) that breaks moiré translation symmetry. At generic fillings, we show how an electric current-induced depinning transition of the crystalline order leads to peculiar nonlinear current-voltage curves consistent with the experiment. At Jain fillings, we propose that the depinning transition is preempted by an equilibrium transition between EIQAH and Jain FQAH states. This transition occurs due to the large polarizability of the Jain FQAH states, which enables them to effectively lower their energy in an applied electric field compared to the crystal states. We also discuss the finite-temperature evolution in terms of the relative entropies of the crystalline and FQAH states.more » « less
-
This work experimentally investigates the pressure-driven flow of a pure Newtonian fluid through three-dimensional (3D) porous media models. The porous media model consists of square arrays of rods that also could be interpreted as a periodic tandem rod arrangement. We employed a time-resolved three-dimensional particle tracking velocimetry (3D Shake-the-Box) technique for a range of Reynolds numbers [Formula: see text] to observe flow structures and vortex formation between the rods in porous media structures with different porosities of [Formula: see text] which corresponds to the spacing ratio of [Formula: see text], where L is the distance between the centers of the rods, and D is the diameter of the rods. For all the examined cases, we further analyzed the effect of the Reynolds number and the spacing ratio on the instantaneous and averaged patterns of velocity, vorticity, and the other flow parameters after obtaining the two-dimensional velocity fields using the bin-averaging method. We observed both symmetrical and asymmetrical patterns of structure and recirculation regions between the rods depending on the Reynolds number and spacing ratio. Increasing the Reynolds number reduced the symmetrical patterns of flow structures with respect to the centerline of the gap region, while the spacing ratio was randomly affecting the symmetry degree. Vortex shedding was considerable for the two examined high Reynolds numbers of Re = 444 and Re = 890 behind the upstream rod as the porosity increased. The backward movement of the reattachment point has been observed by increasing the Reynolds number.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/jfm.2022.209
