Direct numerical simulation of vortex ring evolution from the laminar …

August 1, 2025

Direct numerical simulation is used to study the temporal development of single vortex rings at various Reynolds numbers and core thicknesses. Qualitative differences between the evolution of thin- and thick-core rings are observed leading to a correction factor to the classical equation for the ring translational velocity.

https://eprints.soton.ac.uk/52010/1/direct_numerical_simulation_of_vortex_ring_evolution_from_the_laminar_to_the_early_turbulent_regime.pdf

Direct numerical simulation of vortex ring evolution from the laminar … <body> <h1> Array ( [0] => sirect numerical simulation of vortex ring evolution from the laminar … [1] => xirect numerical simulation of vortex ring evolution from the laminar … [2] => cirect numerical simulation of vortex ring evolution from the laminar … [3] => firect numerical simulation of vortex ring evolution from the laminar … [4] => rirect numerical simulation of vortex ring evolution from the laminar … [5] => eirect numerical simulation of vortex ring evolution from the laminar … [6] => durect numerical simulation of vortex ring evolution from the laminar … [7] => djrect numerical simulation of vortex ring evolution from the laminar … [8] => dkrect numerical simulation of vortex ring evolution from the laminar … [9] => dorect numerical simulation of vortex ring evolution from the laminar … [10] => d9rect numerical simulation of vortex ring evolution from the laminar … [11] => d8rect numerical simulation of vortex ring evolution from the laminar … [12] => dieect numerical simulation of vortex ring evolution from the laminar … [13] => didect numerical simulation of vortex ring evolution from the laminar … [14] => difect numerical simulation of vortex ring evolution from the laminar … [15] => ditect numerical simulation of vortex ring evolution from the laminar … [16] => di5ect numerical simulation of vortex ring evolution from the laminar … [17] => di4ect numerical simulation of vortex ring evolution from the laminar … [18] => dirwct numerical simulation of vortex ring evolution from the laminar … [19] => dirsct numerical simulation of vortex ring evolution from the laminar … [20] => dirdct numerical simulation of vortex ring evolution from the laminar … [21] => dirrct numerical simulation of vortex ring evolution from the laminar … [22] => dir4ct numerical simulation of vortex ring evolution from the laminar … [23] => dir3ct numerical simulation of vortex ring evolution from the laminar … [24] => dirext numerical simulation of vortex ring evolution from the laminar … [25] => direvt numerical simulation of vortex ring evolution from the laminar … [26] => direft numerical simulation of vortex ring evolution from the laminar … [27] => diredt numerical simulation of vortex ring evolution from the laminar … [28] => direcr numerical simulation of vortex ring evolution from the laminar … [29] => direcf numerical simulation of vortex ring evolution from the laminar … [30] => direcg numerical simulation of vortex ring evolution from the laminar … [31] => direcy numerical simulation of vortex ring evolution from the laminar … [32] => direc6 numerical simulation of vortex ring evolution from the laminar … [33] => direc5 numerical simulation of vortex ring evolution from the laminar … [34] => direct bumerical simulation of vortex ring evolution from the laminar … [35] => direct mumerical simulation of vortex ring evolution from the laminar … [36] => direct jumerical simulation of vortex ring evolution from the laminar … [37] => direct humerical simulation of vortex ring evolution from the laminar … [38] => direct nymerical simulation of vortex ring evolution from the laminar … [39] => direct nhmerical simulation of vortex ring evolution from the laminar … [40] => direct njmerical simulation of vortex ring evolution from the laminar … [41] => direct nimerical simulation of vortex ring evolution from the laminar … [42] => direct n8merical simulation of vortex ring evolution from the laminar … [43] => direct n7merical simulation of vortex ring evolution from the laminar … [44] => direct nunerical simulation of vortex ring evolution from the laminar … [45] => direct nukerical simulation of vortex ring evolution from the laminar … [46] => direct nujerical simulation of vortex ring evolution from the laminar … [47] => direct numwrical simulation of vortex ring evolution from the laminar … [48] => direct numsrical simulation of vortex ring evolution from the laminar … [49] => direct numdrical simulation of vortex ring evolution from the laminar … [50] => direct numrrical simulation of vortex ring evolution from the laminar … [51] => direct num4rical simulation of vortex ring evolution from the laminar … [52] => direct num3rical simulation of vortex ring evolution from the laminar … [53] => direct numeeical simulation of vortex ring evolution from the laminar … [54] => direct numedical simulation of vortex ring evolution from the laminar … [55] => direct numefical simulation of vortex ring evolution from the laminar … [56] => direct numetical simulation of vortex ring evolution from the laminar … [57] => direct nume5ical simulation of vortex ring evolution from the laminar … [58] => direct nume4ical simulation of vortex ring evolution from the laminar … [59] => direct numerucal simulation of vortex ring evolution from the laminar … [60] => direct numerjcal simulation of vortex ring evolution from the laminar … [61] => direct numerkcal simulation of vortex ring evolution from the laminar … [62] => direct numerocal simulation of vortex ring evolution from the laminar … [63] => direct numer9cal simulation of vortex ring evolution from the laminar … [64] => direct numer8cal simulation of vortex ring evolution from the laminar … [65] => direct numerixal simulation of vortex ring evolution from the laminar … [66] => direct numerival simulation of vortex ring evolution from the laminar … [67] => direct numerifal simulation of vortex ring evolution from the laminar … [68] => direct numeridal simulation of vortex ring evolution from the laminar … [69] => direct numericzl simulation of vortex ring evolution from the laminar … [70] => direct numericsl simulation of vortex ring evolution from the laminar … [71] => direct numericwl simulation of vortex ring evolution from the laminar … [72] => direct numericql simulation of vortex ring evolution from the laminar … [73] => direct numericak simulation of vortex ring evolution from the laminar … [74] => direct numericap simulation of vortex ring evolution from the laminar … [75] => direct numericao simulation of vortex ring evolution from the laminar … [76] => direct numerical aimulation of vortex ring evolution from the laminar … [77] => direct numerical zimulation of vortex ring evolution from the laminar … [78] => direct numerical ximulation of vortex ring evolution from the laminar … [79] => direct numerical dimulation of vortex ring evolution from the laminar … [80] => direct numerical eimulation of vortex ring evolution from the laminar … [81] => direct numerical wimulation of vortex ring evolution from the laminar … [82] => direct numerical sumulation of vortex ring evolution from the laminar … [83] => direct numerical sjmulation of vortex ring evolution from the laminar … [84] => direct numerical skmulation of vortex ring evolution from the laminar … [85] => direct numerical somulation of vortex ring evolution from the laminar … [86] => direct numerical s9mulation of vortex ring evolution from the laminar … [87] => direct numerical s8mulation of vortex ring evolution from the laminar … [88] => direct numerical sinulation of vortex ring evolution from the laminar … [89] => direct numerical sikulation of vortex ring evolution from the laminar … [90] => direct numerical sijulation of vortex ring evolution from the laminar … [91] => direct numerical simylation of vortex ring evolution from the laminar … [92] => direct numerical simhlation of vortex ring evolution from the laminar … [93] => direct numerical simjlation of vortex ring evolution from the laminar … [94] => direct numerical similation of vortex ring evolution from the laminar … [95] => direct numerical sim8lation of vortex ring evolution from the laminar … [96] => direct numerical sim7lation of vortex ring evolution from the laminar … [97] => direct numerical simukation of vortex ring evolution from the laminar … [98] => direct numerical simupation of vortex ring evolution from the laminar … [99] => direct numerical simuoation of vortex ring evolution from the laminar … [100] => direct numerical simulztion of vortex ring evolution from the laminar … [101] => direct numerical simulstion of vortex ring evolution from the laminar … [102] => direct numerical simulwtion of vortex ring evolution from the laminar … [103] => direct numerical simulqtion of vortex ring evolution from the laminar … [104] => direct numerical simularion of vortex ring evolution from the laminar … [105] => direct numerical simulafion of vortex ring evolution from the laminar … [106] => direct numerical simulagion of vortex ring evolution from the laminar … [107] => direct numerical simulayion of vortex ring evolution from the laminar … [108] => direct numerical simula6ion of vortex ring evolution from the laminar … [109] => direct numerical simula5ion of vortex ring evolution from the laminar … [110] => direct numerical simulatuon of vortex ring evolution from the laminar … [111] => direct numerical simulatjon of vortex ring evolution from the laminar … [112] => direct numerical simulatkon of vortex ring evolution from the laminar … [113] => direct numerical simulatoon of vortex ring evolution from the laminar … [114] => direct numerical simulat9on of vortex ring evolution from the laminar … [115] => direct numerical simulat8on of vortex ring evolution from the laminar … [116] => direct numerical simulatiin of vortex ring evolution from the laminar … [117] => direct numerical simulatikn of vortex ring evolution from the laminar … [118] => direct numerical simulatiln of vortex ring evolution from the laminar … [119] => direct numerical simulatipn of vortex ring evolution from the laminar … [120] => direct numerical simulati0n of vortex ring evolution from the laminar … [121] => direct numerical simulati9n of vortex ring evolution from the laminar … [122] => direct numerical simulatiob of vortex ring evolution from the laminar … [123] => direct numerical simulatiom of vortex ring evolution from the laminar … [124] => direct numerical simulatioj of vortex ring evolution from the laminar … [125] => direct numerical simulatioh of vortex ring evolution from the laminar … [126] => direct numerical simulation if vortex ring evolution from the laminar … [127] => direct numerical simulation kf vortex ring evolution from the laminar … [128] => direct numerical simulation lf vortex ring evolution from the laminar … [129] => direct numerical simulation pf vortex ring evolution from the laminar … [130] => direct numerical simulation 0f vortex ring evolution from the laminar … [131] => direct numerical simulation 9f vortex ring evolution from the laminar … [132] => direct numerical simulation od vortex ring evolution from the laminar … [133] => direct numerical simulation oc vortex ring evolution from the laminar … [134] => direct numerical simulation ov vortex ring evolution from the laminar … [135] => direct numerical simulation og vortex ring evolution from the laminar … [136] => direct numerical simulation ot vortex ring evolution from the laminar … [137] => direct numerical simulation or vortex ring evolution from the laminar … [138] => direct numerical simulation of cortex ring evolution from the laminar … [139] => direct numerical simulation of bortex ring evolution from the laminar … [140] => direct numerical simulation of gortex ring evolution from the laminar … [141] => direct numerical simulation of fortex ring evolution from the laminar … [142] => direct numerical simulation of virtex ring evolution from the laminar … [143] => direct numerical simulation of vkrtex ring evolution from the laminar … [144] => direct numerical simulation of vlrtex ring evolution from the laminar … [145] => direct numerical simulation of vprtex ring evolution from the laminar … [146] => direct numerical simulation of v0rtex ring evolution from the laminar … [147] => direct numerical simulation of v9rtex ring evolution from the laminar … [148] => direct numerical simulation of voetex ring evolution from the laminar … [149] => direct numerical simulation of vodtex ring evolution from the laminar … [150] => direct numerical simulation of voftex ring evolution from the laminar … [151] => direct numerical simulation of vottex ring evolution from the laminar … [152] => direct numerical simulation of vo5tex ring evolution from the laminar … [153] => direct numerical simulation of vo4tex ring evolution from the laminar … [154] => direct numerical simulation of vorrex ring evolution from the laminar … [155] => direct numerical simulation of vorfex ring evolution from the laminar … [156] => direct numerical simulation of vorgex ring evolution from the laminar … [157] => direct numerical simulation of voryex ring evolution from the laminar … [158] => direct numerical simulation of vor6ex ring evolution from the laminar … [159] => direct numerical simulation of vor5ex ring evolution from the laminar … [160] => direct numerical simulation of vortwx ring evolution from the laminar … [161] => direct numerical simulation of vortsx ring evolution from the laminar … [162] => direct numerical simulation of vortdx ring evolution from the laminar … [163] => direct numerical simulation of vortrx ring evolution from the laminar … [164] => direct numerical simulation of vort4x ring evolution from the laminar … [165] => direct numerical simulation of vort3x ring evolution from the laminar … [166] => direct numerical simulation of vortez ring evolution from the laminar … [167] => direct numerical simulation of vortec ring evolution from the laminar … [168] => direct numerical simulation of vorted ring evolution from the laminar … [169] => direct numerical simulation of vortes ring evolution from the laminar … [170] => direct numerical simulation of vortex eing evolution from the laminar … [171] => direct numerical simulation of vortex ding evolution from the laminar … [172] => direct numerical simulation of vortex fing evolution from the laminar … [173] => direct numerical simulation of vortex ting evolution from the laminar … [174] => direct numerical simulation of vortex 5ing evolution from the laminar … [175] => direct numerical simulation of vortex 4ing evolution from the laminar … [176] => direct numerical simulation of vortex rung evolution from the laminar … [177] => direct numerical simulation of vortex rjng evolution from the laminar … [178] => direct numerical simulation of vortex rkng evolution from the laminar … [179] => direct numerical simulation of vortex rong evolution from the laminar … [180] => direct numerical simulation of vortex r9ng evolution from the laminar … [181] => direct numerical simulation of vortex r8ng evolution from the laminar … [182] => direct numerical simulation of vortex ribg evolution from the laminar … [183] => direct numerical simulation of vortex rimg evolution from the laminar … [184] => direct numerical simulation of vortex rijg evolution from the laminar … [185] => direct numerical simulation of vortex rihg evolution from the laminar … [186] => direct numerical simulation of vortex rinf evolution from the laminar … [187] => direct numerical simulation of vortex rinv evolution from the laminar … [188] => direct numerical simulation of vortex rinb evolution from the laminar … [189] => direct numerical simulation of vortex rinh evolution from the laminar … [190] => direct numerical simulation of vortex riny evolution from the laminar … [191] => direct numerical simulation of vortex rint evolution from the laminar … [192] => direct numerical simulation of vortex ring wvolution from the laminar … [193] => direct numerical simulation of vortex ring svolution from the laminar … [194] => direct numerical simulation of vortex ring dvolution from the laminar … [195] => direct numerical simulation of vortex ring rvolution from the laminar … [196] => direct numerical simulation of vortex ring 4volution from the laminar … [197] => direct numerical simulation of vortex ring 3volution from the laminar … [198] => direct numerical simulation of vortex ring ecolution from the laminar … [199] => direct numerical simulation of vortex ring ebolution from the laminar … [200] => direct numerical simulation of vortex ring egolution from the laminar … [201] => direct numerical simulation of vortex ring efolution from the laminar … [202] => direct numerical simulation of vortex ring evilution from the laminar … [203] => direct numerical simulation of vortex ring evklution from the laminar … [204] => direct numerical simulation of vortex ring evllution from the laminar … [205] => direct numerical simulation of vortex ring evplution from the laminar … [206] => direct numerical simulation of vortex ring ev0lution from the laminar … [207] => direct numerical simulation of vortex ring ev9lution from the laminar … [208] => direct numerical simulation of vortex ring evokution from the laminar … [209] => direct numerical simulation of vortex ring evopution from the laminar … [210] => direct numerical simulation of vortex ring evooution from the laminar … [211] => direct numerical simulation of vortex ring evolytion from the laminar … [212] => direct numerical simulation of vortex ring evolhtion from the laminar … [213] => direct numerical simulation of vortex ring evoljtion from the laminar … [214] => direct numerical simulation of vortex ring evolition from the laminar … [215] => direct numerical simulation of vortex ring evol8tion from the laminar … [216] => direct numerical simulation of vortex ring evol7tion from the laminar … [217] => direct numerical simulation of vortex ring evolurion from the laminar … [218] => direct numerical simulation of vortex ring evolufion from the laminar … [219] => direct numerical simulation of vortex ring evolugion from the laminar … [220] => direct numerical simulation of vortex ring evoluyion from the laminar … [221] => direct numerical simulation of vortex ring evolu6ion from the laminar … [222] => direct numerical simulation of vortex ring evolu5ion from the laminar … [223] => direct numerical simulation of vortex ring evolutuon from the laminar … [224] => direct numerical simulation of vortex ring evolutjon from the laminar … [225] => direct numerical simulation of vortex ring evolutkon from the laminar … [226] => direct numerical simulation of vortex ring evolutoon from the laminar … [227] => direct numerical simulation of vortex ring evolut9on from the laminar … [228] => direct numerical simulation of vortex ring evolut8on from the laminar … [229] => direct numerical simulation of vortex ring evolutiin from the laminar … [230] => direct numerical simulation of vortex ring evolutikn from the laminar … [231] => direct numerical simulation of vortex ring evolutiln from the laminar … [232] => direct numerical simulation of vortex ring evolutipn from the laminar … [233] => direct numerical simulation of vortex ring evoluti0n from the laminar … [234] => direct numerical simulation of vortex ring evoluti9n from the laminar … [235] => direct numerical simulation of vortex ring evolutiob from the laminar … [236] => direct numerical simulation of vortex ring evolutiom from the laminar … [237] => direct numerical simulation of vortex ring evolutioj from the laminar … [238] => direct numerical simulation of vortex ring evolutioh from the laminar … [239] => direct numerical simulation of vortex ring evolution drom the laminar … [240] => direct numerical simulation of vortex ring evolution crom the laminar … [241] => direct numerical simulation of vortex ring evolution vrom the laminar … [242] => direct numerical simulation of vortex ring evolution grom the laminar … [243] => direct numerical simulation of vortex ring evolution trom the laminar … [244] => direct numerical simulation of vortex ring evolution rrom the laminar … [245] => direct numerical simulation of vortex ring evolution feom the laminar … [246] => direct numerical simulation of vortex ring evolution fdom the laminar … [247] => direct numerical simulation of vortex ring evolution ffom the laminar … [248] => direct numerical simulation of vortex ring evolution ftom the laminar … [249] => direct numerical simulation of vortex ring evolution f5om the laminar … [250] => direct numerical simulation of vortex ring evolution f4om the laminar … [251] => direct numerical simulation of vortex ring evolution frim the laminar … [252] => direct numerical simulation of vortex ring evolution frkm the laminar … [253] => direct numerical simulation of vortex ring evolution frlm the laminar … [254] => direct numerical simulation of vortex ring evolution frpm the laminar … [255] => direct numerical simulation of vortex ring evolution fr0m the laminar … [256] => direct numerical simulation of vortex ring evolution fr9m the laminar … [257] => direct numerical simulation of vortex ring evolution fron the laminar … [258] => direct numerical simulation of vortex ring evolution frok the laminar … [259] => direct numerical simulation of vortex ring evolution froj the laminar … [260] => direct numerical simulation of vortex ring evolution from rhe laminar … [261] => direct numerical simulation of vortex ring evolution from fhe laminar … [262] => direct numerical simulation of vortex ring evolution from ghe laminar … [263] => direct numerical simulation of vortex ring evolution from yhe laminar … [264] => direct numerical simulation of vortex ring evolution from 6he laminar … [265] => direct numerical simulation of vortex ring evolution from 5he laminar … [266] => direct numerical simulation of vortex ring evolution from tge laminar … [267] => direct numerical simulation of vortex ring evolution from tbe laminar … [268] => direct numerical simulation of vortex ring evolution from tne laminar … [269] => direct numerical simulation of vortex ring evolution from tje laminar … [270] => direct numerical simulation of vortex ring evolution from tue laminar … [271] => direct numerical simulation of vortex ring evolution from tye laminar … [272] => direct numerical simulation of vortex ring evolution from thw laminar … [273] => direct numerical simulation of vortex ring evolution from ths laminar … [274] => direct numerical simulation of vortex ring evolution from thd laminar … [275] => direct numerical simulation of vortex ring evolution from thr laminar … [276] => direct numerical simulation of vortex ring evolution from th4 laminar … [277] => direct numerical simulation of vortex ring evolution from th3 laminar … [278] => direct numerical simulation of vortex ring evolution from the kaminar … [279] => direct numerical simulation of vortex ring evolution from the paminar … [280] => direct numerical simulation of vortex ring evolution from the oaminar … [281] => direct numerical simulation of vortex ring evolution from the lzminar … [282] => direct numerical simulation of vortex ring evolution from the lsminar … [283] => direct numerical simulation of vortex ring evolution from the lwminar … [284] => direct numerical simulation of vortex ring evolution from the lqminar … [285] => direct numerical simulation of vortex ring evolution from the laninar … [286] => direct numerical simulation of vortex ring evolution from the lakinar … [287] => direct numerical simulation of vortex ring evolution from the lajinar … [288] => direct numerical simulation of vortex ring evolution from the lamunar … [289] => direct numerical simulation of vortex ring evolution from the lamjnar … [290] => direct numerical simulation of vortex ring evolution from the lamknar … [291] => direct numerical simulation of vortex ring evolution from the lamonar … [292] => direct numerical simulation of vortex ring evolution from the lam9nar … [293] => direct numerical simulation of vortex ring evolution from the lam8nar … [294] => direct numerical simulation of vortex ring evolution from the lamibar … [295] => direct numerical simulation of vortex ring evolution from the lamimar … [296] => direct numerical simulation of vortex ring evolution from the lamijar … [297] => direct numerical simulation of vortex ring evolution from the lamihar … [298] => direct numerical simulation of vortex ring evolution from the laminzr … [299] => direct numerical simulation of vortex ring evolution from the laminsr … [300] => direct numerical simulation of vortex ring evolution from the laminwr … [301] => direct numerical simulation of vortex ring evolution from the laminqr … [302] => direct numerical simulation of vortex ring evolution from the laminae … [303] => direct numerical simulation of vortex ring evolution from the laminad … [304] => direct numerical simulation of vortex ring evolution from the laminaf … [305] => direct numerical simulation of vortex ring evolution from the laminat … [306] => direct numerical simulation of vortex ring evolution from the lamina5 … [307] => direct numerical simulation of vortex ring evolution from the lamina4 … [308] => direct numerical simulation of vortex ring evolution from the laminar ᰾ [309] => direct numerical simulation of vortex ring evolution from the laminar &#u230; [310] => direct numerical simulation of vortex ring evolution from the laminar &#i230; [311] => direct numerical simulation of vortex ring evolution from the laminar ␎ [312] => direct numerical simulation of vortex ring evolution from the laminar ῂ [313] => direct numerical simulation of vortex ring evolution from the laminar &#8q30; [314] => direct numerical simulation of vortex ring evolution from the laminar &#8w30; [315] => direct numerical simulation of vortex ring evolution from the laminar ₊ [316] => direct numerical simulation of vortex ring evolution from the laminar “ [317] => direct numerical simulation of vortex ring evolution from the laminar &#82w0; [318] => direct numerical simulation of vortex ring evolution from the laminar &#82e0; [319] => direct numerical simulation of vortex ring evolution from the laminar ‰ [320] => direct numerical simulation of vortex ring evolution from the laminar   [321] => direct numerical simulation of vortex ring evolution from the laminar &#823o; [322] => direct numerical simulation of vortex ring evolution from the laminar &#823p; [323] => direct numerical simulation of vortex ring evolution from the laminar &#823-; ) https://clipperroutesevere.com/kdjbw4ywu?key=a54852e5dee5f9fa314d768d692142d1 </h1> </body>