%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%% The data in this file are extracted from a direct numerical simulation of a turbulent pipe flow %%%% Numerical method: openpipeflow www.openpipeflow.org/ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % % Grid (streamwise) nz = 1024 % Grid (wall-normal) ny = 192 % Grid (azimuthal) nz = 256 % Streamwise domain size Lz = 10pi % bulk Reynolds number Re_b (= U_b*D/nu)=5300 % Friction vel u_tau = 0.034187384148816% Re_tau Re_tau = 1.811931359887262e+02%% All data speficied with a ^+ are normalized by u_tau and nu % This file was last updated on 11/04/2020.% %------------------------------------------------------------------------------------------------------------------------------------------------------------------------------%% R 1-R (1-R)^+ Uz^+ P^+ dUz/dy^+ %%-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------%1 0 0 0 2.35771611594603e-17 -1.000029676068990.999940658285739 5.93417142608077e-05 0.0107523113018627 0.0107523113018627 -8.41800554640980e-11 -0.9999703239310150.999762647079131 0.000237352920869349 0.0430067200684014 0.0430028915569538 -5.27302609473378e-09 -0.9997922070816150.999466008185429 0.000533991814570700 0.0967556514743755 0.0967326742420018 -6.22935995900943e-08 -0.9994948267244260.999050811269150 0.000949188730850259 0.171986482787917 0.171909820864314 -3.67845870805511e-07 -0.9990764083192950.998517153837707 0.00148284616229299 0.268681546334715 0.268489479148101 -1.48660170832015e-06 -0.9985324363981640.997865161218517 0.00213483878148291 0.386818133647239 0.386413136742544 -4.72337024602902e-06 -0.9978535388421870.997094986529564 0.00290501347043592 0.526368500797778 0.525607247922922 -1.26899822919573e-05 -0.9970226650361570.996206810643442 0.00379318935655826 0.687299874913849 0.685980702418257 -3.00881730914030e-05 -0.9960115239515910.995200842144875 0.00479915785512508 0.869574461875042 0.867420595874381 -6.46977910968286e-05 -0.9947763011743570.994077317281735 0.00592268271826468 1.07314945518861 1.06978566564296 -0.000128520974577548 -0.9932527750138010.992836499909560 0.00716350009044031 1.29797704604240 1.29289670033894 -0.000238995457869974 -0.9913511098822810.991478681429584 0.00852131857041638 1.54400443453271 1.53652325621416 -0.000420162055606494 -0.9889508168932560.990004180720307 0.00999581927969273 1.81117384206410 1.80036616617345 -0.000703659150392739 -0.9858966131524770.988413344062608 0.0115866559373916 2.09942252491838 2.08403565533933 -0.00112942405418317 -0.9819961317087030.986706545058419 0.0132934549415810 2.40868278898988 2.38702540877951 -0.00174600697343427 -0.9770205582341710.984884184542987 0.0151158154570129 2.73888200568303 2.70868365997640 -0.00261044345759987 -0.9707092140495300.982946690490741 0.0170533095092591 3.08994262896902 3.04818321132507 -0.00378767886008955 -0.9627788033056400.980894517914782 0.0191054820852176 3.46178221359700 3.40449312483786 -0.00534958489319196 -0.9529374813722120.978728148760027 0.0212718512399728 3.85431343445634 3.77635544928789 -0.00737364652907843 -0.9409031417451170.976448091790023 0.0235519082099767 4.26744410708430 4.16227058804518 -0.00994142147937394 -0.9264244956812230.974054882467469 0.0259451175325307 4.70107720931532 4.56049461524301 -0.0131368818821406 -0.9093028186605910.971549082828463 0.0284509171715375 5.15511090406637 4.96905097210831 -0.0170447384462730 -0.8894118462886330.968931281350508 0.0310687186494922 5.62943856325292 5.38575760565170 -0.0217488241792675 -0.8667133408156480.966202092814315 0.0337979071856847 6.12394879283011 5.80826895284428 -0.0273305829599355 -0.8412663292857270.963362158159422 0.0366378418405783 6.63852545895334 6.23413049848347 -0.0338676739686432 -0.8132288335548640.960412144333668 0.0395878556663316 7.17304771525169 6.66084221867075 -0.0414326729364142 -0.7828518962568690.957352744136570 0.0426472558634302 7.72739003120851 7.08592627912237 -0.0500918321332554 -0.7504666664882270.954184676056615 0.0458153239433853 8.30142222164135 7.50699400825021 -0.0599038587654764 -0.7164660911447460.950908684102530 0.0490913158974705 8.89500947727589 7.92180742625779 -0.0709186873364216 -0.6812832663228900.947525537628552 0.0524744623714485 9.50801239640516 8.32833140767037 -0.0831762488980940 -0.6453686941046270.944036031153750 0.0559639688462505 10.1402870176275 8.72477373248111 -0.0967052663885216 -0.6091685635224000.940440984175433 0.0595590158245669 10.7916848536554 9.10961163543314 -0.111522120990911 -0.5731057820525450.936741240976698 0.0632587590233025 11.4620529261873 9.48160478400057 -0.127629840888286 -0.5375649276008370.932937670428147 0.0670623295718529 12.1512338018335 9.83979573656572 -0.145017268764713 -0.5028816871169480.929031165783843 0.0709688342161571 12.8590656290895 10.1834997475262 -0.163658473255800 -0.4693367880428320.925022644471528 0.0749773555284722 13.5853821763455 10.5122862477036 -0.183512477195373 -0.4371539744595110.920913047877170 0.0790869521228304 14.3300128709259 10.8259544452245 -0.204523362482456 -0.4065012760831320.916703341123882 0.0832966588761177 15.0927828391469 11.1245053303318 -0.226620769633455 -0.3774946929431050.912394512845269 0.0876054871547314 15.8735129473858 11.4081120401516 -0.249720764056020 -0.3502034575793420.907987574953245 0.0920124250467554 16.6720198441492 11.6770901584721 -0.273727015195792 -0.3246561858031740.903483562400395 0.0965164375996046 17.4881160031326 11.9318691772576 -0.298532232741835 -0.3008474257803070.898883532936921 0.101116467063079 18.3216097672601 12.1729660819927 -0.324019827781614 -0.2787442844882280.894188566862226 0.105811433137774 19.1723053936947 12.4009618100494 -0.350065807579017 -0.2582928934597020.889399766771218 0.110600233228782 20.0400030998075 12.6164811119732 -0.376540922601738 -0.2394244601966370.884518257295366 0.115481742704634 20.9244991100958 12.8201760352411 -0.403313000600982 -0.2220605168000060.879545184838585 0.120454815161415 21.8255857040392 13.0127127188282 -0.430249288981323 -0.2061169100915150.874481717308007 0.125518282691994 22.7430512648818 13.1947606584767 -0.457218649506195 -0.1915064614392590.869329043839702 0.130670956160298 23.6766803293298 13.3669836803664 -0.484093561206455 -0.1781408404021510.864088374519417 0.135911625480583 24.6262536381521 13.5300324828439 -0.510751878814277 -0.1659322305035560.858760940098388 0.141239059901612 25.5915481876726 13.6845388850995 -0.537078205972969 -0.1547947827176780.853347991704307 0.146652008295693 26.5723372821413 13.8311115599453 -0.562964805228015 -0.1446455547008690.847850800547493 0.152149199452507 27.5683905869739 13.9703327332525 -0.588312127210325 -0.1354049768196350.842270657622361 0.157729342377639 28.5794741828439 14.1027555950845 -0.613029127959457 -0.1269971151308450.836608873404231 0.163391126595769 29.6053506206184 14.2289023441515 -0.637033504315618 -0.1193497688254990.830866777541570 0.169133222458430 30.6457789771218 14.3492626354618 -0.660251956695397 -0.1123944310553510.825045718543729 0.174954281456271 31.7005149117161 14.4642923811007 -0.682620605495410 -0.1060664051130010.819147063464250 0.180852936535750 32.7693107236826 14.5744132671799 -0.704085478341646 -0.1003053464439160.813172197579822 0.186827802420178 33.8519154103942 14.6800135443397 -0.724602831551660 -0.09505614940446950.807122524064948 0.192877475935052 34.9480747262622 14.7814503508503 -0.744139095384904 -0.09026954715431920.800999463662420 0.199000536337580 36.0575312424446 14.8790527824920 -0.762670388405851 -0.08590160025001850.794804454349661 0.205195545650339 37.1800244073028 14.9731240695483 -0.780181725502302 -0.08191218312406720.788538951001021 0.211461048998979 38.3152906075906 15.0639421348058 -0.796665981633706 -0.07826379461174350.782204425046107 0.217795574953893 39.4630632303635 15.1517597560203 -0.812122919837419 -0.07492167300251800.775802364124222 0.224197635875778 40.6230727255908 15.2368059195191 -0.826558558772253 -0.07185463059930900.769334271734997 0.230665728265003 41.7950466694592 15.3192884379611 -0.839984876425977 -0.06903552172743010.762801666885304 0.237198333114696 42.9787098283502 15.3993969875701 -0.852419852409979 -0.06644102708813310.756206083732521 0.243793916267479 44.1737842234774 15.4773058258471 -0.863887442941375 -0.06405075900601700.749549071224239 0.250450928775761 45.3799891961693 15.5531752384655 -0.874417049226338 -0.06184596752353370.742832192734498 0.257167807265502 46.5970414737806 15.6271515613091 -0.884042502692587 -0.05980872269031450.736057025696641 0.263942974303359 47.8246552362174 15.6993669187176 -0.892800836873594 -0.05792210012693590.729225161232849 0.270774838767151 49.0625421830618 15.7699398948844 -0.900731081130905 -0.05617096020520930.722338203780481 0.277661796219519 50.3104116012773 15.8389774047927 -0.907873234631350 -0.05454251478849890.715397770715273 0.284602229284727 51.5679704334822 15.9065770432625 -0.914267473020828 -0.05302630089502220.708405491971506 0.291594508028494 52.8349233467726 15.9728291887158 -0.919953488639840 -0.05161369479062410.701363009659221 0.298636990340780 54.1109728020808 16.0378183973254 -0.924970002505569 -0.05029705993405690.694271977678574 0.305728022321426 55.3958191240504 16.1016235428113 -0.929354586972043 -0.04906877574285300.687134061331430 0.312865938668570 56.6891605714147 16.1643168408291 -0.933143760124326 -0.04792081642895420.679950936930265 0.320049063069735 57.9906934078589 16.2259629473582 -0.936373272706288 -0.04684503654510120.672724291404497 0.327275708595504 59.3001119733518 16.2866187413546 -0.939078494529991 -0.04583361681253420.665455821904312 0.334544178095689 60.6171087559287 16.3463336279135 -0.941294654626848 -0.04487953088342640.658147235402098 0.341852764597902 61.9413744639096 16.4051506252332 -0.943056467582618 -0.04397707513117260.650800248291571 0.349199751708429 63.2725980985348 16.4631081749179 -0.944397043856634 -0.04312239731134570.643416585984679 0.356583414015321 64.6104670270023 16.5202427704693 -0.945347182242005 -0.04231414636045840.635997982506404 0.364002017493597 65.9546670558879 16.5765926639846 -0.945935586806781 -0.04155320063581270.628546180087526 0.371453819912474 67.3048825049327 16.6321999254172 -0.946189077231215 -0.04084014175715030.621062928755472 0.378937071244528 68.6607962811793 16.6871074381540 -0.946132787025958 -0.04017209184544840.613549985923327 0.386450014076673 70.0220899534397 16.7413523529989 -0.945791091667792 -0.03954225561344320.606009115977110 0.393990884022890 71.3884438270780 16.7949616739999 -0.945188983578717 -0.03894286185773470.598442089861416 0.401557910138584 72.7595370190892 16.8479535990800 -0.944352864168013 -0.03836879795512080.590850684663518 0.409149315336482 74.1350475334573 16.9003430736867 -0.943309682011512 -0.03781889668541400.583236683196025 0.416763316803975 75.5146523367752 16.9521468195653 -0.942084579989567 -0.03729417254625220.575601873578191 0.424398126421809 76.8980274341074 17.0033841933865 -0.940698697506125 -0.03679496133207420.567948048815988 0.432051951184013 78.2848479450793 17.0540743833963 -0.939168577568762 -0.03631959552851690.560277006381018 0.439722993618983 79.6747881801741 17.1042335727900 -0.937507373833034 -0.03586498085178740.552590547788392 0.447409452211608 81.0675217172195 17.1538736816973 -0.935726755581797 -0.03542721135021060.544890478173644 0.455109521826356 82.4627214780470 17.2030012135282 -0.933838127417423 -0.03500175721000460.537178605868808 0.462821394131192 83.8600598053048 17.2516165226735 -0.931852720678248 -0.03458439072013960.529456741977732 0.470543258022268 85.2592085394071 17.2997152647978 -0.929781001657566 -0.03417218886879830.521726699950751 0.478273300049249 86.6598390956005 17.3472905016270 -0.927631873524402 -0.03376332364647990.513990295158803 0.486009704841197 88.0616225411316 17.3943336058727 -0.925412221552677 -0.03335650352303540.506249344467100 0.493750655532900 89.4642296724955 17.4408348313318 -0.923127044252753 -0.03295084458403670.498505665808437 0.501494334191563 90.8673310927475 17.4867838720068 -0.920779870079468 -0.03254561308019470.490761077756266 0.509238922243734 92.2705972888613 17.5321697191693 -0.918373327135888 -0.03213972589464580.483017399097603 0.516982600902397 93.6736987091133 17.5769798249438 -0.915909759217473 -0.03173139969943860.475276448405900 0.524723551594100 95.0763058404772 17.6211989813525 -0.913391920046206 -0.03131830277105180.467540043613952 0.532459956386048 96.4780892860084 17.6648089208355 -0.910824007069013 -0.03089845453202670.459810001586971 0.540189998413029 97.8787198422018 17.7077897312918 -0.908212793791967 -0.03047143109515320.452088137695895 0.547911862304105 99.2778685763039 17.7501228403752 -0.905568190312430 -0.03003897379678530.444376265391059 0.555623734608941 100.675206903562 17.7917941193566 -0.902903053913699 -0.02960452678559760.436676195776312 0.563323804223688 102.070406664389 17.8327955380114 -0.900232315867340 -0.02917201292867710.428989737183686 0.571010262816315 103.463140201435 17.8731248074551 -0.897571483927611 -0.02874453333153820.421318694748716 0.578681305251284 104.853080436530 17.9127833823191 -0.894935268288258 -0.02832348169623890.413664869986512 0.586335130013488 106.239900947501 17.9517736427878 -0.892336913944039 -0.02790828949529550.406030060368678 0.593969939631322 107.623276044834 17.9900962249677 -0.889787711996796 -0.02749686377338420.398416058901185 0.601583941098815 109.002880848151 18.0277484712348 -0.887296377535548 -0.02708662092054850.390824653703287 0.609175346296713 110.378391362520 18.0647246688639 -0.884868632342316 -0.02667565309584360.383257627587594 0.616742372412406 111.749484554531 18.1010177372024 -0.882507252807931 -0.02626337865820400.375716757641376 0.624283242358624 113.115838428169 18.1366212344076 -0.880212736561476 -0.02585036413086260.368203814809231 0.631796185190770 114.477132100430 18.1715305099135 -0.877984211755823 -0.02543759485708730.360720563477177 0.639279436522823 115.833045876676 18.2057426751688 -0.875820089520512 -0.02502596851375080.353268761058299 0.646731238941701 117.183261325721 18.2392563557289 -0.873718615085782 -0.02461634698805570.345850157580024 0.654149842419976 118.527461354607 18.2720717980146 -0.871678252934717 -0.02420961283880910.338466495273132 0.661533504726868 119.865330283074 18.3041907712365 -0.869697596391263 -0.02380644483430940.331119508162605 0.668880491837395 121.196553917699 18.3356160692220 -0.867775049584669 -0.02340713574555320.323810921660392 0.676189078339609 122.520819625680 18.3663509353965 -0.865908405482648 -0.02301150580412420.316542452160206 0.683457547839794 123.837816408257 18.3963983594328 -0.864094348063268 -0.02261884285530630.309315806634438 0.690684193365562 125.147234973750 18.4257603775510 -0.862329271232263 -0.02222803698707100.302132682233273 0.697867317766727 126.448767810194 18.4544377604738 -0.860610822033311 -0.02183772218658180.294994765886129 0.705005234113871 127.742109257558 18.4824297193038 -0.858937412818023 -0.02144638035479240.287903733905483 0.712096266094517 129.026955579528 18.5097338878713 -0.857306974503757 -0.02105272372291020.280861251593197 0.719138748406803 130.303005034836 18.5363470256909 -0.855717709839630 -0.02065598634234050.273868972849430 0.726131027150570 131.569957948127 18.5622657338352 -0.854169590985499 -0.02025578393784350.266928539784222 0.733071460215778 132.827516780332 18.5874867662594 -0.852664208259740 -0.01985199164482630.260041582331854 0.739958417668146 134.075386198547 18.6120074040299 -0.851203249909207 -0.01944497526505250.253209717868062 0.746790282131938 135.313273145391 18.6358263142866 -0.849787726171983 -0.01903569651753610.246434550830205 0.753565449169796 136.540886907828 18.6589441400582 -0.848418604717316 -0.01862529868457200.239717672340465 0.760282327659535 137.757939185439 18.6813632866093 -0.847097560077243 -0.01821469309517450.233060659832182 0.766939340167818 138.964144158131 18.7030874798871 -0.845827215453175 -0.01780450821112830.226465076679399 0.773534923320601 140.159218553259 18.7241214463238 -0.844610983212953 -0.01739518534531830.219932471829706 0.780067528170294 141.342881712150 18.7444707250757 -0.843452496323431 -0.01698705584542930.213464379440482 0.786535620559518 142.514855656018 18.7641415478786 -0.842354937516140 -0.01658032036736590.207062318518596 0.792937681481404 143.674865151245 18.7831406149100 -0.841320594596127 -0.01617491475262110.200727792563682 0.799272207436318 144.822637774018 18.8014746800020 -0.840350706046544 -0.01577041033232780.194462289215042 0.805537710784958 145.957903974306 18.8191501287104 -0.839445534644688 -0.01536609386955590.188267279902283 0.811732720097717 147.080397139164 18.8361727875832 -0.838604602744104 -0.01496116661743170.182144219499755 0.817855780500245 148.189853655347 18.8525479846719 -0.837827006087485 -0.01455490827142110.176094545984881 0.823905454015119 149.286012971215 18.8682807362263 -0.837111621014408 -0.01414677205061150.170119680100453 0.829880319899547 150.368617657926 18.8833760080901 -0.836457107976791 -0.01373644636952730.164221025020975 0.835778974979025 151.437413469893 18.8978390150077 -0.835861787535386 -0.01332385452837590.158399966023133 0.841600033976867 152.492149404487 18.9116754522897 -0.835323506571981 -0.01290907562863460.152657870160472 0.847342129839528 153.532577760990 18.9248915982334 -0.834839568298129 -0.01249225755101770.146996085942342 0.853003914057658 154.558454198765 18.9374943429397 -0.834406746056324 -0.01207359532410060.141415943017210 0.858584056982790 155.569537794635 18.9494912346102 -0.834021368769481 -0.01165337099436510.135918751860396 0.864081248139604 156.565591099467 18.9608905796419 -0.833679459680387 -0.01123200534350550.130505803466315 0.869494196533685 157.546380193936 18.9717015768170 -0.833376908739345 -0.01081009061599760.125178369045286 0.874821630954714 158.511674743457 18.9819344583761 -0.833109649052117 -0.01038840572843360.119937699725001 0.880062300274999 159.461248052279 18.9916006244497 -0.832873800501208 -0.009967914898893590.114785026256697 0.885214973743303 160.394877116727 19.0007127493404 -0.832665753959643 -0.009549733182812390.109721558726118 0.890278441273882 161.312342677570 19.0092848194217 -0.832482194801040 -0.009135050492548100.104748486269337 0.895251513730663 162.213429271513 19.0173320729889 -0.832320089287126 -0.008725036327395350.0998669767934851 0.900133023206515 163.097925281801 19.0248708509114 -0.832176667369995 -0.008320759991316290.0950781767024774 0.904921823297523 163.965622987914 19.0319183946365 -0.832049424921892 -0.007923142935479060.0903832106277826 0.909616789372217 164.816318614349 19.0384926266184 -0.831936144610954 -0.007532937849174190.0857831811643078 0.914216818835692 165.649812378476 19.0446119339054 -0.831834913939578 -0.007150725040665740.0812791686114586 0.918720831388541 166.465908537460 19.0502949681565 -0.831744116729597 -0.006776924676064350.0768722307194345 0.923127769280566 167.264415434223 19.0555604762484 -0.831662392382574 -0.006411826355615350.0725634024408208 0.927436597559179 168.045145542462 19.0604271731988 -0.831588580131468 -0.006055628713167300.0683536956875334 0.931646304312467 168.807915510683 19.0649136560468 -0.831521673814205 -0.005708471387096760.0642440990931753 0.935755900906825 169.552546205263 19.0690383411485 -0.831460801120826 -0.005370444030665130.0602355777808601 0.939764422219140 170.278862752519 19.0728194024109 -0.831405222444217 -0.005041572839054070.0563290731365562 0.943670926863444 170.986694579775 19.0762746988982 -0.831354334554141 -0.004721800744380060.0525255025880055 0.947474497411995 171.675875455422 19.0794216974367 -0.831307667250714 -0.004410980381438910.0488257593892701 0.951174240610730 172.346243527953 19.0822774064324 -0.831264869409565 -0.004108889264824840.0452307124109537 0.954769287589046 172.997641363981 19.0848583359903 -0.831225686862128 -0.003815263651421220.0417412059361516 0.958258794063848 173.629915985204 19.0871804903457 -0.831189936570776 -0.003529839717067470.0383580594621737 0.961641940537826 174.242918904333 19.0892593884776 -0.831157481122939 -0.003252390285303240.0350820675080883 0.964917932491912 174.836506159967 19.0911101024640 -0.831128206336911 -0.002982749927579130.0319139994281332 0.968086000571867 175.410538350400 19.0927473019111 -0.831102003572130 -0.002720826936942280.0288545992310349 0.971145400768965 175.964880666357 19.0941852952075 -0.831078757381960 -0.002466604652655860.0259045854052813 0.974095414594719 176.499402922656 19.0954380620789 -0.831058338389786 -0.002220135982831610.0230646507503878 0.976935349249612 177.013979588779 19.0965192751418 -0.831040600668999 -0.001981534383418560.0203354622141953 0.979664537785805 177.508489818356 19.0974423101641 -0.831025382509167 -0.001750963231456810.0177176607362406 0.982282339263759 177.982817477542 19.0982202456837 -0.831012509312583 -0.001528624432108370.0152118610972338 0.984788138902766 178.436851172294 19.0988658530064 -0.831001797478708 -0.001314746586466000.0128186517746798 0.987181348225320 178.870484274525 19.0993915778173 -0.830993058415225 -0.001109573023717450.0105385948046759 0.989461405195324 179.283614947152 19.0998095148726 -0.830986102150096 -0.0009133501942535580.00837222564992074 0.991627774350079 179.676146168012 19.1001313775013 -0.830980740314847 -0.0007263170859504430.00632005307396212 0.993679946926038 180.047985752640 19.1003684638403 -0.830976788475537 -0.0005486963339932660.00438255902171608 0.995617440978284 180.399046375926 19.1005316217698 -0.830974067898166 -0.0003806875362430110.00256019850628406 0.997439801493716 180.729245592619 19.1006312143721 -0.830972406871335 -0.0002224630145614740.000853399502094686 0.999146600497905 181.038505856690 19.1006770874213 -0.830971641701531 -7.42000518717481e-05