Xu, Duo; Song, Baofang; Avila, Marc (2021): Optimal perturbation (helical, Re=2000,A=1,Wo=15): u_z profile t=tf [dataset]. PANGAEA, https://doi.org/10.1594/PANGAEA.932554
Always quote citation above when using data! You can download the citation in several formats below.
Published: 2021-06-11 • DOI registered: 2022-12-31
Abstract:
The data are obtained via an in-house Matlab script (developed by Dr. Baofang Song) to compute the non-modal transient growth of disturbances in pulsatile and oscillatory pipe flows. In this study, a Newtonian fluid driven by pulsatile and oscillatory flow rate flows in a straight pipe. In pulsatile flow, there are three governing parameters: steady Reynolds number (defined by the steady flow component), pulsation amplitude (ratio of oscillatory and steady flow component) and Womersley number (dimensionless pulsation and oscillation frequency). In oscillatory flow, due to vanishment of steady flow component, oscillatory Reynolds number (defined by the oscillation flow component) and Womersley number. The Reynolds number defined by the thickness of Stokes layer is alternatively used for the oscillatory Reynolds number. The study was carried out in a manner that one governing parameter varies while other governing parameters are fixed.
The data file 'Uz_profile_helical.dat' shows the streamwise velocity profile corresponding to the optimal helical perturbation.
This file includes two columns: the first column 'r' indicates radial coordinate; the second column 'uz' indicates streamwise velocity.
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
Comment:
VARIABLES = "r", "uz"
ZONE T="helical, tf", I=201, J=1
Parameter(s):
| # | Name | Short Name | Unit | Principal Investigator | Method/Device | Comment |
|---|---|---|---|---|---|---|
| 1 | Radial co-ordinate | r | Xu, Duo | |||
| 2 | u_z, velocity, cylindrical, axial component | u_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:
402 data points
Data
| 1 r | 2 u_z |
|---|---|
| 1.00000000000000000000000000000000 | 0.00000000000000000000000000000000 |
| 0.99996900285358550000000000000000 | 0.00029214561453182837000000000000 |
| 0.99987601333598820000000000000000 | 0.00116830882924123350000000000000 |
| 0.99972103721202740000000000000000 | 0.00262766753122188000000000000000 |
| 0.99950408408933840000000000000000 | 0.00466884746442015000000000000000 |
| 0.99922516741777660000000000000000 | 0.00728991619638994300000000000000 |
| 0.99888430448858380000000000000000 | 0.01048837480822902700000000000000 |
| 0.99848151643331620000000000000000 | 0.01426114744272022700000000000000 |
| 0.99801682822253460000000000000000 | 0.01860456888210192500000000000000 |
| 0.99749026866425580000000000000000 | 0.02351437036184249300000000000000 |
| 0.99690187040216740000000000000000 | 0.02898566385973085000000000000000 |
| 0.99625166991360350000000000000000 | 0.03501292513038388000000000000000 |
| 0.99553970750728360000000000000000 | 0.04158997578351738000000000000000 |
| 0.99476602732081350000000000000000 | 0.04870996472974352400000000000000 |
| 0.99393067731794950000000000000000 | 0.05636534934000009000000000000000 |
| 0.99303370928562410000000000000000 | 0.06454787668374978000000000000000 |
| 0.99207517883073600000000000000000 | 0.07324856522648820000000000000000 |
| 0.99105514537670330000000000000000 | 0.08245768737878478000000000000000 |
| 0.98997367215977840000000000000000 | 0.09216475329681179000000000000000 |
| 0.98883082622512850000000000000000 | 0.10235849633792288000000000000000 |
| 0.98762667842267940000000000000000 | 0.11302686057423433000000000000000 |
| 0.98636130340272230000000000000000 | 0.12415699076235251000000000000000 |
| 0.98503477961128700000000000000000 | 0.13573522515803899000000000000000 |
| 0.98364718928527770000000000000000 | 0.14774709155114435000000000000000 |
| 0.98219861844737540000000000000000 | 0.16017730687813195000000000000000 |
| 0.98068915690070480000000000000000 | 0.17300978074741719000000000000000 |
| 0.97911889822326710000000000000000 | 0.18622762318635020000000000000000 |
| 0.97748793976213850000000000000000 | 0.19981315688846144000000000000000 |
| 0.97579638262743560000000000000000 | 0.21374793420532645000000000000000 |
| 0.97404433168604650000000000000000 | 0.22801275908984603000000000000000 |
| 0.97223189555513060000000000000000 | 0.24258771415665123000000000000000 |
| 0.97035918659538380000000000000000 | 0.25745219298144020000000000000000 |
| 0.96842632090407390000000000000000 | 0.27258493771439780000000000000000 |
| 0.96643341830784270000000000000000 | 0.28796408203409950000000000000000 |
| 0.96438060235527700000000000000000 | 0.30356719941762280000000000000000 |
| 0.96226800030925040000000000000000 | 0.31937135665060984000000000000000 |
| 0.96009574313903270000000000000000 | 0.33535317244825624000000000000000 |
| 0.95786396551217080000000000000000 | 0.35148888100493460000000000000000 |
| 0.95557280578614080000000000000000 | 0.36775440023719097000000000000000 |
| 0.95322240599976930000000000000000 | 0.38412540443260270000000000000000 |
| 0.95081291186442920000000000000000 | 0.40057740096586540000000000000000 |
| 0.94834447275500530000000000000000 | 0.41708581069441630000000000000000 |
| 0.94581724170063460000000000000000 | 0.43362605159896990000000000000000 |
| 0.94323137537521940000000000000000 | 0.45017362519053150000000000000000 |
| 0.94058703408771360000000000000000 | 0.46670420516497050000000000000000 |
| 0.93788438177218540000000000000000 | 0.48319372774972990000000000000000 |
| 0.93512358597765390000000000000000 | 0.49961848315520074000000000000000 |
| 0.93230481785770190000000000000000 | 0.51595520751608010000000000000000 |
| 0.92942825215986580000000000000000 | 0.53218117468604400000000000000000 |
| 0.92649406721480180000000000000000 | 0.54827428723280300000000000000000 |
| 0.92350244492523050000000000000000 | 0.56421316597013320000000000000000 |
| 0.92045357075466030000000000000000 | 0.57997723735921940000000000000000 |
| 0.91734763371588910000000000000000 | 0.59554681811371870000000000000000 |
| 0.91418482635928740000000000000000 | 0.61090319635141970000000000000000 |
| 0.91096534476086060000000000000000 | 0.62602870865037820000000000000000 |
| 0.90768938851009360000000000000000 | 0.64090681238879040000000000000000 |
| 0.90435716069757750000000000000000 | 0.65552215277566920000000000000000 |
| 0.90096886790241910000000000000000 | 0.66986062401327540000000000000000 |
| 0.89752472017943420000000000000000 | 0.68390942407213440000000000000000 |
| 0.89402493104612520000000000000000 | 0.69765710260487970000000000000000 |
| 0.89046971746944460000000000000000 | 0.71109360157581370000000000000000 |
| 0.88685929985234370000000000000000 | 0.72421028823843240000000000000000 |
| 0.88319390202010970000000000000000 | 0.73699998015278400000000000000000 |
| 0.87947375120648910000000000000000 | 0.74945696199776310000000000000000 |
| 0.87569907803960080000000000000000 | 0.76157699399971130000000000000000 |
| 0.87187011652763840000000000000000 | 0.77335731186733190000000000000000 |
| 0.86798710404436310000000000000000 | 0.78479661819318940000000000000000 |
| 0.86405028131438790000000000000000 | 0.79589506535328080000000000000000 |
| 0.86005989239825390000000000000000 | 0.80665423000753000000000000000000 |
| 0.85601618467730010000000000000000 | 0.81707707937485160000000000000000 |
| 0.85191940883832710000000000000000 | 0.82716792952590430000000000000000 |
| 0.84776981885805580000000000000000 | 0.83693239600400300000000000000000 |
| 0.84356767198738270000000000000000 | 0.84637733714925360000000000000000 |
| 0.83931322873543120000000000000000 | 0.85551079056201880000000000000000 |
| 0.83500675285340240000000000000000 | 0.86434190319872930000000000000000 |
| 0.83064851131822290000000000000000 | 0.87288085564518330000000000000000 |
| 0.82623877431599490000000000000000 | 0.88113878115925990000000000000000 |
| 0.82177781522524520000000000000000 | 0.88912768011595330000000000000000 |
| 0.81726591059997800000000000000000 | 0.89686033052233070000000000000000 |
| 0.81270334015253000000000000000000 | 0.90435019529814190000000000000000 |
| 0.80809038673622950000000000000000 | 0.91161132703902980000000000000000 |
| 0.80342733632786120000000000000000 | 0.91865827099345370000000000000000 |
| 0.79871447800993790000000000000000 | 0.92550596699142180000000000000000 |
| 0.79395210395277800000000000000000 | 0.93216965106292120000000000000000 |
| 0.78914050939639360000000000000000 | 0.93866475747657630000000000000000 |
| 0.78427999263218640000000000000000 | 0.94500682191474820000000000000000 |
| 0.77937085498445600000000000000000 | 0.95121138648018700000000000000000 |
| 0.77441340079171940000000000000000 | 0.95729390720182750000000000000000 |
| 0.76940793738784330000000000000000 | 0.96326966467371070000000000000000 |
| 0.76435477508299190000000000000000 | 0.96915367842180260000000000000000 |
| 0.75925422714438870000000000000000 | 0.97496062554916610000000000000000 |
| 0.75410660977689630000000000000000 | 0.98070476416107090000000000000000 |
| 0.74891224210341310000000000000000 | 0.98639986201885140000000000000000 |
| 0.74367144614508970000000000000000 | 0.99205913081524090000000000000000 |
| 0.73838454680136540000000000000000 | 0.99769516640522850000000000000000 |
| 0.73305187182982630000000000000000 | 1.00331989526591200000000000000000 |
| 0.72767375182588620000000000000000 | 1.00894452739699440000000000000000 |
| 0.72225052020229140000000000000000 | 1.01457951581129580000000000000000 |
| 0.71678251316845130000000000000000 | 1.02023452270251450000000000000000 |
| 0.71127006970959500000000000000000 | 1.02591839231624320000000000000000 |
| 0.70571353156575680000000000000000 | 1.03163913049050300000000000000000 |
| 0.70011324321058920000000000000000 | 1.03740389077446520000000000000000 |
| 0.69446955183000870000000000000000 | 1.04321896697913500000000000000000 |
| 0.68878280730067120000000000000000 | 1.04908979196210030000000000000000 |
| 0.68305336216828200000000000000000 | 1.05502094240049300000000000000000 |
| 0.67728157162574110000000000000000 | 1.06101614926244410000000000000000 |
| 0.67146779349112100000000000000000 | 1.06707831364793360000000000000000 |
| 0.66561238818548600000000000000000 | 1.07320952763527070000000000000000 |
| 0.65971571871054720000000000000000 | 1.07941109973976970000000000000000 |
| 0.65377815062615870000000000000000 | 1.08568358456659770000000000000000 |
| 0.64780005202765520000000000000000 | 1.09202681622038970000000000000000 |
| 0.64178179352303160000000000000000 | 1.09843994502004480000000000000000 |
| 0.63572374820996800000000000000000 | 1.10492147705810200000000000000000 |
| 0.62962629165269960000000000000000 | 1.11146931614010860000000000000000 |
| 0.62348980185873360000000000000000 | 1.11808080764031210000000000000000 |
| 0.61731465925541520000000000000000 | 1.12475278381555780000000000000000 |
| 0.61110124666634340000000000000000 | 1.13148161012923500000000000000000 |
| 0.60484994928763750000000000000000 | 1.13826323215114460000000000000000 |
| 0.59856115466405800000000000000000 | 1.14509322261691750000000000000000 |
| 0.59223525266498010000000000000000 | 1.15196682825174230000000000000000 |
| 0.58587263546022480000000000000000 | 1.15887901598721180000000000000000 |
| 0.57947369749574630000000000000000 | 1.16582451822671550000000000000000 |
| 0.57303883546917860000000000000000 | 1.17279787684349520000000000000000 |
| 0.56656844830524230000000000000000 | 1.17979348562587160000000000000000 |
| 0.56006293713101430000000000000000 | 1.18680563091573270000000000000000 |
| 0.55352270525105910000000000000000 | 1.19382853021882740000000000000000 |
| 0.54694815812242690000000000000000 | 1.20085636859819500000000000000000 |
| 0.54033970332951790000000000000000 | 1.20788333269489630000000000000000 |
| 0.53369775055881350000000000000000 | 1.21490364225265110000000000000000 |
| 0.52702271157347890000000000000000 | 1.22191157905471080000000000000000 |
| 0.52031500018783540000000000000000 | 1.22890151321197800000000000000000 |
| 0.51357503224170680000000000000000 | 1.23586792677074420000000000000000 |
| 0.50680322557464000000000000000000 | 1.24280543463618500000000000000000 |
| 0.50000000000000010000000000000000 | 1.24970880283373380000000000000000 |
| 0.49316577727894556000000000000000 | 1.25657296415443700000000000000000 |
| 0.48630098109428140000000000000000 | 1.26339303125226000000000000000000 |
| 0.47940603702419220000000000000000 | 1.27016430728094120000000000000000 |
| 0.47248137251585953000000000000000 | 1.27688229417527930000000000000000 |
| 0.46552741685896310000000000000000 | 1.28354269869671530000000000000000 |
| 0.45854460115906600000000000000000 | 1.29014143637563900000000000000000 |
| 0.45153335831088950000000000000000 | 1.29667463349310140000000000000000 |
| 0.44449412297147570000000000000000 | 1.30313862725256700000000000000000 |
| 0.43742733153324154000000000000000 | 1.30952996429806980000000000000000 |
| 0.43033342209692510000000000000000 | 1.31584539773875360000000000000000 |
| 0.42321283444442503000000000000000 | 1.32208188284138500000000000000000 |
| 0.41606601001153726000000000000000 | 1.32823657155217020000000000000000 |
| 0.40889339186058880000000000000000 | 1.33430680600722560000000000000000 |
| 0.40169542465296937000000000000000 | 1.34029011118750960000000000000000 |
| 0.39447255462156605000000000000000 | 1.34618418686908200000000000000000 |
| 0.38722522954309857000000000000000 | 1.35198689901339320000000000000000 |
| 0.37995389871036000000000000000000 | 1.35769627073507680000000000000000 |
| 0.37265901290436326000000000000000 | 1.36331047297662340000000000000000 |
| 0.36534102436639520000000000000000 | 1.36882781501049800000000000000000 |
| 0.35800038676997986000000000000000 | 1.37424673487989320000000000000000 |
| 0.35063755519275447000000000000000 | 1.37956578987956370000000000000000 |
| 0.34325298608825560000000000000000 | 1.38478364716819510000000000000000 |
| 0.33584713725762250000000000000000 | 1.38989907459366000000000000000000 |
| 0.32842046782121670000000000000000 | 1.39491093180245280000000000000000 |
| 0.32097343819015756000000000000000 | 1.39981816169467600000000000000000 |
| 0.31350651003778110000000000000000 | 1.40461978227627250000000000000000 |
| 0.30602014627101765000000000000000 | 1.40931487895087780000000000000000 |
| 0.29851481100169464000000000000000 | 1.41390259728476080000000000000000 |
| 0.29099096951776460000000000000000 | 1.41838213626989670000000000000000 |
| 0.28344908825445970000000000000000 | 1.42275274210235030000000000000000 |
| 0.27588963476537520000000000000000 | 1.42701370248584850000000000000000 |
| 0.26831307769348480000000000000000 | 1.43116434146375500000000000000000 |
| 0.26071988674208580000000000000000 | 1.43520401477660940000000000000000 |
| 0.25311053264568200000000000000000 | 1.43913210573700350000000000000000 |
| 0.24548548714079924000000000000000 | 1.44294802160880400000000000000000 |
| 0.23784522293674118000000000000000 | 1.44665119047362230000000000000000 |
| 0.23019021368628464000000000000000 | 1.45024105856391560000000000000000 |
| 0.22252093395631445000000000000000 | 1.45371708803920980000000000000000 |
| 0.21483785919840400000000000000000 | 1.45707875517959540000000000000000 |
| 0.20714146571933964000000000000000 | 1.46032554896882830000000000000000 |
| 0.19943223065159246000000000000000 | 1.46345697003808930000000000000000 |
| 0.19171063192373850000000000000000 | 1.46647252994058590000000000000000 |
| 0.18397714823083083000000000000000 | 1.46937175072675920000000000000000 |
| 0.17623225900472170000000000000000 | 1.47215416478981730000000000000000 |
| 0.16847644438434214000000000000000 | 1.47481931495157650000000000000000 |
| 0.16071018518593438000000000000000 | 1.47736675475917980000000000000000 |
| 0.15293396287324584000000000000000 | 1.47979604896407450000000000000000 |
| 0.14514825952767943000000000000000 | 1.48210677415565770000000000000000 |
| 0.13735355781840825000000000000000 | 1.48429851952320480000000000000000 |
| 0.12955034097245258000000000000000 | 1.48637088772101930000000000000000 |
| 0.12173909274472254000000000000000 | 1.48832349581319260000000000000000 |
| 0.11392029738802815000000000000000 | 1.49015597627584780000000000000000 |
| 0.10609443962305812000000000000000 | 1.49186797803630890000000000000000 |
| 0.09826200460833055000000000000000 | 1.49345916753018850000000000000000 |
| 0.09042347791011557000000000000000 | 1.49492922975895870000000000000000 |
| 0.08257934547233240000000000000000 | 1.49627786933210680000000000000000 |
| 0.07473009358642417000000000000000 | 1.49750481147948110000000000000000 |
| 0.06687620886121122000000000000000 | 1.49860980302089160000000000000000 |
| 0.05901817819272284000000000000000 | 1.49959261328143410000000000000000 |
| 0.05115648873401335000000000000000 | 1.50045303494232040000000000000000 |
| 0.04329162786496118000000000000000 | 1.50119088481829980000000000000000 |
| 0.03542408316205411000000000000000 | 1.50180600455392520000000000000000 |
| 0.02755434236816206000000000000000 | 1.50229826123207480000000000000000 |
| 0.01968289336230075500000000000000 | 1.50266754788920130000000000000000 |
| 0.01181022412938440400000000000000 | 1.50291378393280170000000000000000 |
| 0.00393682272997522100000000000000 | 1.50303691545756300000000000000000 |
| 0.00000000000000000000000000000000 | 1.50303691545756300000000000000000 |
