Coherent structures in interacting vortex rings

Deng, Jian; Xue, Jingyu; Mao, Xuerui; Caulfield, C. P.

doi:10.1103/physrevfluids.2.022701

Cited by 9 publications

(15 citation statements)

References 30 publications

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“…As shown in figure 4, all the ω r structures correspond to ω θ ω r < 0 and therefore undergo growth. As the ω r component corresponds to finger structures extending from the ring centre to the core, this vorticity amplification mechanism also explains the coherent finger-like structures observed by Deng et al (2017). For both the Orr and vorticity-amplification mechanisms addressed above, which correspond to two-and three-dimensional perturbation amplifications, respectively, the transient growth is associated with the base flow outside the vortex core.…”

Section: The Orr Mechanismmentioning

confidence: 72%

“…Examples can be found in the propulsion of fish and salps, through the undulatory motion of the body and tail or the ejection of fluid through an orifice; aquatic mammals such as dolphins and whales have been observed to produce vortex rings, via exhalation of air through their blowholes; in insect flapping flights, vortex rings are produced to generate lift (Linden & Turber 2004;Wang & Wu 2010;Lim & Adhikari 2015); the shedding of vortex rings has been observed in an oscillating-disk flow and an impulsively started jet (Gharib, Rambod & Shariff 1998;Deng et al 2017). Vortex rings also have a significant role in acoustic noise generation in jet flows, mixing in reactors and combustors and the control of separation in synthetic jet flows (Hussain & Husain 1989;Asato et al 1997;Jabbal & Zhong 2010).…”

Section: Introductionmentioning

confidence: 99%

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Optimal transient growth on a vortex ring and its transition via cascade of ringlets

Mao

Hussain

2017

J. Fluid Mech.

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Linear and nonlinear transient growths of perturbations on a vortex ring up to Reynolds number (≡ circulation/viscosity) Re = 27 000 are studied. For short time intervals, perturbations around the ring axis undergo the strongest linear transient growth and lead to secondary structures in the form of ringlets, owing to the Orr mechanism and an inviscid vorticity-amplification mechanism: in contrast to the well-reported instabilities and lobe structures along the vortex ring core. These secondary ringlet structures induce a tertiary group of ringlets through similar transient perturbation growth. This cascade of ringlets lead to the breakup of the main ring even before activation of the vortex-core instabilities. Such a cascade scenario is also observed in the development of a vortex ring perturbed by random disturbance in the axis region. These new modes and mechanisms for the generation and breakup of vortex ring structures bring insights into the dynamics and control of vortex ring flows.

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Section: The Orr Mechanismmentioning

confidence: 72%

Section: Introductionmentioning

confidence: 99%

Optimal transient growth on a vortex ring and its transition via cascade of ringlets

Mao

Hussain

2017

J. Fluid Mech.

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“…In section 2, we briefly review our numerical methods both for direct simulation and Floquet stability analysis, and describe the specific parameters for our simulations. In section 3, we present our results, particularly placing them into the context of our previous two-dimensional and Floquet instability studies, described in and Deng et al (2017). We then draw our conclusions in section 4.…”

Section: Introductionmentioning

confidence: 84%

“…It is at least plausible that the higher wavenumber (i.e. with m > 1) instabilities discussed in and Deng et al (2017) occur strongly only when the spheroid is sufficiently 'thin', thus allowing excitation of sufficiently fine scale perturbations, although this has not been established by detailed analysis.…”

Section: Unidirectional Locomotionmentioning

confidence: 99%

“…Branch 'I' occurs for smaller KC (and typically at lower wavenumber m) for given β, and thus branch 'I' is the first symmetry-breaking instability to occur as the amplitude of the oscillation increases. Finite amplitude manifestations of these instabilities have been observed experimentally (Deng et al 2017) once again only for the relatively small aspect ratio AR = 0.1, and so it is naturally of interest to investigate whether these instabilities, particularly for such smaller aspect ratio spheroids, play any role in any symmetry-breaking leading (at finite amplitude) to locomotion. In such an investigation it is always important to remember two aspects of the evidence from our two-dimensional studies.…”

Section: Introductionmentioning

confidence: 99%

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Horizontal locomotion of a vertically flapping oblate spheroid

Deng

Caulfield

2018

J. Fluid Mech.

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We consider the self-induced motions of three-dimensional oblate spheroids of density $\unicode[STIX]{x1D70C}_{s}$ with varying aspect ratios $AR=b/c\leqslant 1$, where $b$ and $c$ are the spheroids’ centre-pole radius and centre-equator radius, respectively. Vertical motion is imposed on the spheroids such that $y_{s}(t)=A\sin (2\unicode[STIX]{x03C0}ft)$ in a fluid of density $\unicode[STIX]{x1D70C}$ and kinematic viscosity $\unicode[STIX]{x1D708}$. As in strictly two-dimensional flows, above a critical value $Re_{C}$ of the flapping Reynolds number $Re_{A}=2Afc/\unicode[STIX]{x1D708}$, the spheroid ultimately propels itself horizontally as a result of fluid–body interactions. For $Re_{A}$ sufficiently above $Re_{C}$, the spheroid rapidly settles into a terminal state of constant, unidirectional velocity, consistent with the prediction of Deng et al. (Phys. Rev. E, vol. 94, 2016, 033107) that, at sufficiently high $Re_{A}$, such oscillating spheroids manifest $m=1$ asymmetric flow, with characteristic vortical structures conducive to providing unidirectional thrust if the spheroid is free to move horizontally. The speed $U$ of propagation increases linearly with the flapping frequency, resulting in a constant Strouhal number $St(AR)=2Af/U$, characterising the locomotive performance of the oblate spheroid, somewhat larger than the equivalent $St$ for two-dimensional spheroids, demonstrating that the three-dimensional flow is less efficient at driving locomotion. $St$ decreases with increasing aspect ratio for both two-dimensional and three-dimensional flows, although the relative disparity (and hence relative inefficiency of three-dimensional motion) decreases. For flows with $Re_{A}\gtrsim Re_{C}$, we observe two distinct types of inherently three-dimensional motion for different aspect ratios. The first, associated with a disk of aspect ratio $AR=0.1$ at $Re_{A}=45$, consists of a ‘stair-step’ trajectory. This trajectory can be understood through consideration of relatively high azimuthal wavenumber instabilities of interacting vortex rings, characterised by in-phase vortical structures above and below an oscillating spheroid, recently calculated using Floquet analysis by Deng et al. (Phys. Rev. E, vol. 94, 2016, 033107). Such ‘in-phase’ instabilities arise in a relatively narrow band of $Re_{A}\gtrsim Re_{C}$, which band shifts to higher Reynolds number as the aspect ratio increases. (Indeed, for horizontally fixed spheroids with aspect ratio $AR=0.2$, Floquet analysis actually predicts stability at $Re_{A}=45$.) For such a spheroid ($AR=0.2$, $Re_{A}=45$, with sufficiently small mass ratio $m_{s}/m_{f}=\unicode[STIX]{x1D70C}_{s}V_{s}/(\unicode[STIX]{x1D70C}V_{s})$, where $V_{s}$ is the volume of the spheroid) which is free to move horizontally, the second type of three-dimensional motion is observed, initially taking the form of a ‘snaking’ trajectory with long quasi-periodic sweeping oscillations before locking into an approximately elliptical ‘orbit’, apparently manifesting a three-dimensional generalisation of the $QP_{H}$ quasi-periodic symmetry breaking discussed for sufficiently high aspect ratio two-dimensional elliptical foils in Deng & Caulfield (J. Fluid Mech., vol. 787, 2016, pp. 16–49).

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