Citation:

PANGAEA.929197

Name: Optimal perturbation (classic, Re=2000,A=1,Wo=15): Time series of the r-theta-z-components contributions to the kinetic energy and enstrophy
Published: 2021-03-16
License: https://creativecommons.org/licenses/by/4.0/
Keywords: nonlinear instability; transition to turbulence

Always quote citation above when using data! You can download the citation in several formats below.

Published: 2021-03-16 • DOI registered: 2022-12-31

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Abstract:

Laminar flows through pipes driven at steady, pulsatile or oscillatory rates undergo a subcritical transition to turbulence. We carry out an extensive linear non-modal stability analysis of these flows and show that for sufficiently high pulsation amplitudes the stream-wise vortices of the classic lift-up mechanism are outperformed by helical disturbances exhibiting an Orr-like mechanism. In oscillatory flow, the energy amplification depends solely on the Reynolds number based on the Stokes-layer thickness, and for sufficiently high oscillation frequency and Reynolds number, axisymmetric disturbances dominate. In the high-frequency limit, these axisymmetric disturbances are exactly similar to those recently identified by Biau (J. Fluid Mech., vol. 794, 2016, R4) for oscillatory flow over a flat plate. In all regimes of pulsatile and oscillatory pipe flow, the optimal helical and axisymmetric disturbances are triggered in the deceleration phase and reach their peaks in typically less than a period. Their maximum energy gain scales exponentially with Reynolds number of the oscillatory flow component. Our numerical computations unveil a plausible mechanism for the turbulence observed experimentally in pulsatile and oscillatory pipe flow.

Keyword(s):

nonlinear instability; transition to turbulence

Related to:

Xu, Duo; Song, Baofang; Avila, Marc (accepted): Non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. Journal of Fluid Mechanics, 907, https://doi.org/10.1017/jfm.2020.940

Event(s):

FLUID_SIMULATION_MODELING (FSM) * Method/Device: Model simulation

Comment:

OptimalPerturbation_classic_time_vel_vort

#(k_op,m_op)=(0.00000000,1)

VARIABLES = "t", "t/T", "ur", "ut", "uz", "curlr", "curlt", "curlz"

ZONE T="time series", I=16755, J=1

Parameter(s):

#	Name	Short Name	Principal Investigator
1	Dimensionless time	t	Xu, Duo
2	Time by pulsation period	t/T	Xu, Duo
3	Velocity, radial	ur	Xu, Duo
4	u_θ, velocity, cylindrical, azimuthal component	u_θ	Xu, Duo
5	u_z, velocity, cylindrical, axial component	u_z	Xu, Duo
6	Curl of velocity, radial direction	Curl-r	Xu, Duo
7	Curl of velocity, azimuthal direction	Curl-t	Xu, Duo
8	Curl of velocity, axial direction	Curl-z	Xu, Duo

License:

Creative Commons Attribution 4.0 International (CC-BY-4.0)

Status:

Curation Level: Enhanced curation (CurationLevelC) * Processing Level: PANGAEA data processing level 2 (ProcLevel2)

Size:

134040 data points

Data

Download dataset as tab-delimited text — use the following character encoding:

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33.502634000000	0.599862354000	0.233452507000	0.352033702000	61.871470300000	10.462534400000	15.527695800000	2.525097010000
33.512634000000	0.600041403000	0.233392078000	0.351936656000	61.922884900000	10.462534400000	15.527695800000	2.525097010000
33.522634000000	0.600220452000	0.233331665000	0.351839637000	61.974308700000	10.462534400000	15.527695800000	2.525097010000
33.532634000000	0.600399502000	0.233271267000	0.351742647000	62.025741700000	10.462534400000	15.527695800000	2.525097010000
33.542634000000	0.600578551000	0.233210886000	0.351645684000	62.077184000000	10.462534400000	15.527695800000	2.525097010000
33.552634000000	0.600757600000	0.233150521000	0.351548750000	62.128635400000	10.462534400000	15.527695800000	2.525097010000
33.562634000000	0.600936650000	0.233090172000	0.351451843000	62.180096000000	10.462534400000	15.527695800000	2.525097010000
33.572634000000	0.601115699000	0.233029839000	0.351354964000	62.231565700000	10.462534400000	15.527695800000	2.525097010000
33.582634000000	0.601294748000	0.232969522000	0.351258113000	62.283044500000	10.462534400000	15.527695800000	2.525097010000
33.592634000000	0.601473797000	0.232909220000	0.351161289000	62.334532500000	10.462534400000	15.527695800000	2.525097010000
33.602634000000	0.601652847000	0.232848935000	0.351064494000	62.386029600000	10.462534400000	15.527695800000	2.525097010000
33.612634000000	0.601831896000	0.232788666000	0.350967726000	62.437535700000	10.462534400000	15.527695800000	2.525097010000
33.622634000000	0.602010945000	0.232728413000	0.350870986000	62.489051000000	10.462534400000	15.527695800000	2.525097010000
33.632634000000	0.602189995000	0.232668176000	0.350774274000	62.540575200000	10.462534400000	15.527695800000	2.525097010000
33.642634000000	0.602369044000	0.232607955000	0.350677589000	62.592108500000	10.462534400000	15.527695800000	2.525097010000
33.652634000000	0.602548093000	0.232547749000	0.350580933000	62.643650900000	10.462534400000	15.527695800000	2.525097010000
33.662634000000	0.602727143000	0.232487560000	0.350484304000	62.695202200000	10.462534400000	15.527695800000	2.525097010000
33.672634000000	0.602906192000	0.232427387000	0.350387703000	62.746762500000	10.462534400000	15.527695800000	2.525097010000
33.682634000000	0.603085241000	0.232367229000	0.350291130000	62.798331800000	10.462534400000	15.527695800000	2.525097010000
33.692634000000	0.603264291000	0.232307088000	0.350194584000	62.849910100000	10.462534400000	15.527695800000	2.525097010000
33.702634000000	0.603443340000	0.232246963000	0.350098066000	62.901497300000	10.462534400000	15.527695800000	2.525097010000
33.712634000000	0.603622389000	0.232186853000	0.350001576000	62.953093400000	10.462534400000	15.527695800000	2.525097010000
33.722634000000	0.603801438000	0.232126759000	0.349905114000	63.004698400000	10.462534400000	15.527695800000	2.525097010000
33.732634000000	0.603980488000	0.232066682000	0.349808679000	63.056312300000	10.462534400000	15.527695800000	2.525097010000
33.742634000000	0.604159537000	0.232006620000	0.349712272000	63.107935100000	10.462534400000	15.527695800000	2.525097010000
33.752634000000	0.604338586000	0.231946574000	0.349615893000	63.159566800000	10.462534400000	15.527695800000	2.525097010000
33.762634000000	0.604517636000	0.231886544000	0.349519541000	63.211207300000	10.462534400000	15.527695800000	2.525097010000
33.772634000000	0.604696685000	0.231826530000	0.349423217000	63.262856600000	10.462534400000	15.527695800000	2.525097010000
33.782634000000	0.604875734000	0.231766532000	0.349326921000	63.314514700000	10.462534400000	15.527695800000	2.525097010000
33.792634000000	0.605054784000	0.231706550000	0.349230652000	63.366181700000	10.462534400000	15.527695800000	2.525097010000
33.802634000000	0.605233833000	0.231646584000	0.349134411000	63.417857400000	10.462534400000	15.527695800000	2.525097010000
33.812634000000	0.605412882000	0.231586634000	0.349038198000	63.469541900000	10.462534400000	15.527695800000	2.525097010000
33.822634000000	0.605591932000	0.231526699000	0.348942012000	63.521235100000	10.462534400000	15.527695800000	2.525097010000
33.832634000000	0.605770981000	0.231466781000	0.348845854000	63.572937100000	10.462534400000	15.527695800000	2.525097010000
33.842634000000	0.605950030000	0.231406878000	0.348749723000	63.624647800000	10.462534400000	15.527695800000	2.525097010000
33.852634000000	0.606129080000	0.231346991000	0.348653620000	63.676367200000	10.462534400000	15.527695800000	2.525097010000
33.862634000000	0.606308129000	0.231287120000	0.348557545000	63.728095200000	10.462534400000	15.527695800000	2.525097010000
33.872634000000	0.606487178000	0.231227265000	0.348461497000	63.779832000000	10.462534400000	15.527695800000	2.525097010000
33.882634000000	0.606666227000	0.231167426000	0.348365477000	63.831577400000	10.462534400000	15.527695800000	2.525097010000
33.892634000000	0.606845277000	0.231107602000	0.348269485000	63.883331400000	10.462534400000	15.527695800000	2.525097010000
33.902634000000	0.607024326000	0.231047795000	0.348173520000	63.935094100000	10.462534400000	15.527695800000	2.525097010000
33.912634000000	0.607203375000	0.230988003000	0.348077582000	63.986865400000	10.462534400000	15.527695800000	2.525097010000
33.922634000000	0.607382425000	0.230928227000	0.347981672000	64.038645200000	10.462534400000	15.527695800000	2.525097010000
33.932634000000	0.607561474000	0.230868467000	0.347885790000	64.090433700000	10.462534400000	15.527695800000	2.525097010000
33.942634000000	0.607740523000	0.230808723000	0.347789935000	64.142230700000	10.462534400000	15.527695800000	2.525097010000
33.952634000000	0.607919573000	0.230748995000	0.347694107000	64.194036200000	10.462534400000	15.527695800000	2.525097010000
33.962634000000	0.608098622000	0.230689282000	0.347598308000	64.245850300000	10.462534400000	15.527695800000	2.525097010000

Only the first 2000 rows were shown. To view the complete dataset, download it as tab-delimited text. You can still view the full matrix in your browser, but be aware that this may crash the browser due to the huge size.