435:
considered at the temperature being considered. On the other hand, the reference length is always an arbitrary parameter, so particular attention should be put when comparing flows around different obstacles or in channels of different shapes: the global
Reynolds numbers should be referred to the same reference length. This is actually the reason for which the most precise sources for airfoil and channel flow data specify the reference length at the Reynolds number. The reference length can vary depending on the analysis to be performed: for a body with circle sections such as circular cylinders or spheres, one usually chooses the diameter; for an airfoil, a generic non-circular cylinder or a
900:
was first necessary to know the pressure distribution around the cylinder in a steady flow. Much to his surprise, Hiemenz found that the flow in his channel oscillated violently. When he reported this to
Prandtl, the latter told him: 'Obviously your cylinder is not circular.' However, even after very careful machining of the cylinder, the flow continued to oscillate. Then Hiemenz was told that possibly the channel was not symmetric, and he started to adjust it. I was not concerned with this problem, but every morning when I came in the laboratory I asked him, 'Herr Hiemenz, is the flow steady now?' He answered very sadly, 'It always oscillates.'
20:
694:
1959:
110:
547:
94:
69:" of suspended telephone or power lines and the vibration of a car antenna at certain speeds. Mathematical modeling of von Kármán vortex street can be performed using different techniques including but not limited to solving the full Navier-Stokes equations with k-epsilon, SST, k-omega and Reynolds stress, and large eddy simulation (LES) turbulence models, by numerically solving some dynamic equations such as the
1746:
573:
483:≈ 47. Eddies are shed continuously from each side of the circle boundary, forming rows of vortices in its wake. The alternation leads to the core of a vortex in one row being opposite the point midway between two vortex cores in the other row, giving rise to the distinctive pattern shown in the picture. Ultimately, the
598:
434:
For common flows (the ones which can usually be considered as incompressible or isothermal), the kinematic viscosity is everywhere uniform over all the flow field and constant in time, so there is no choice on the viscosity parameter, which becomes naturally the kinematic viscosity of the fluid being
681:
When a tuned mass damper is installed on a cylindrical structure, such as a tall chimney or mast, it helps to reduce the vibration amplitudes caused by vortex shedding. The tuned mass damper consists of a mass that is attached to the structure through springs or dampers. In many cases, the spring is
455:
as the flow speed parameter for comparing different profiles). On the other hand, for fairings and struts the given parameter is usually the dimension of internal structure to be streamlined (let us think for simplicity it is a beam with circular section), and the main target is to minimize the drag
899:
had a doctoral candidate, Karl
Hiemenz, to whom he gave the task of constructing a water channel in which he could observe the separation of the flow behind a cylinder. The object was to check experimentally the separation point calculated by means of the boundary-layer theory. For this purpose, it
617:
In low turbulence, tall buildings can produce a Kármán street, so long as the structure is uniform along its height. In urban areas where there are many other tall structures nearby, the turbulence produced by these can prevent the formation of coherent vortices. Periodic crosswind forces set up by
558:
The flow of atmospheric air over obstacles such as islands or isolated mountains sometimes gives birth to von Kármán vortex streets. When a cloud layer is present at the relevant altitude, the streets become visible. Such cloud layer vortex streets have been photographed from satellites. The vortex
689:
The effectiveness of a tuned mass damper in mitigating vortex shedding-induced vibrations depends on factors such as the mass of the damper, its placement on the structure, and the tuning of the system. Engineers carefully analyze the structural dynamics and characteristics of the vortex shedding
450:
For an aerodynamic profile the reference length depends on the analysis. In fact, the profile chord is usually chosen as the reference length also for aerodynamic coefficient for wing sections and thin profiles in which the primary target is to maximize the lift coefficient or the lift/drag ratio
916:
whilst wading through water. Vortices could be seen in the water, and von Kármán noted that "The problem for historians may have been why
Christopher was carrying Jesus through the water. For me it was why the vortices". It has been suggested by researchers that the painting is one from the 14th
579:
577:
574:
578:
685:
As the structure is subjected to vortex shedding-induced vibrations, the tuned mass damper oscillates in an out-of-phase motion with the structure. This counteracts the vibrations, reducing their amplitudes and minimizing the potential for resonance and structural damage.
576:
604:
602:
599:
603:
456:
coefficient or the drag/lift ratio. The main design parameter which becomes naturally also a reference length is therefore the profile thickness (the profile dimension or area perpendicular to the flow direction), rather than the profile chord.
714:
projections resembling large screw threads are sometimes placed at the top, which effectively create asymmetric three-dimensional flow, thereby discouraging the alternate shedding of vortices; this is also found in some car antennas.
1151:
Farazande, S. and
Bayindir, C., The Interaction of Von Kármán Vortices with the Solitons of the Complex GinzburgLandau Equation. International Conference on Applied Mathematics in Engineering (ICAME) September 1–3, 2021 - Balikesir,
682:
replaced by suspending the mass on cables such that it forms a pendulum system with the same resonance frequency. The mass is carefully tuned to have a natural frequency that matches the dominant frequency of the vortex shedding.
601:
2153:
796:
705:
Another solution to prevent the unwanted vibration of such cylindrical bodies is a longitudinal fin that can be fitted on the downstream side, which, provided it is longer than the diameter of the cylinder, prevents the
256:
like the body speed relative to the fluid at rest, or an inviscid flow speed, computed through the
Bernoulli equation), which is the original global flow parameter, i.e. the target to be non-dimensionalised.
1282:
200:
89:
Animation of vortex street created by a cylindrical object; the flow on opposite sides of the object is given different colors, showing that the vortices are shed from alternating sides of the object
366:
86:
575:
836:
718:
Another countermeasure with tall buildings is using variation in the diameter with height, such as tapering - that prevents the entire building from being driven at the same frequency.
622:
caused, which can damage the structure, hence it is important for engineers to account for the possible effects of vortex shedding when designing a wide range of structures, from
1805:
637:. For monitoring such engineering structures, the efficient measurements of von Kármán streets can be performed using smart sensing algorithms such as compressive sensing.
678:(TMD). A tuned mass damper is a device consisting of a mass-spring system that is specifically designed and tuned to counteract the vibrations induced by vortex shedding.
600:
254:
396:
735:
425:
305:
710:
from interacting, and consequently they remain attached. Obviously, for a tall building or mast, the relative wind could come from any direction. For this reason,
1470:
276:
223:
105:
mountains. This phenomenon observed from ground level is extremely rare, as most cloud-related Kármán vortex street activity is viewed from space.
1770:"Flow visualisation of the vortex shedding mechanism on circular cylinder using hydrogen bubbles illuminated by a laser sheet in a water channel"
1750:
1376:
Etling, D. (1990-03-01). "Mesoscale vortex shedding from large islands: A comparison with laboratory experiments of rotating stratified flows".
26:
of the vortex street behind a circular cylinder in air; the flow is made visible through release of glycerol vapour in the air near the cylinder
559:
street can reach over 400 km (250 mi) from the obstacle and the diameter of the vortices are normally 20–40 km (12–25 mi).
1161:
Monkewitz, P. A., Williamson, C. H. K. and Miller, G. D., Phase dynamics of Kármán vortices in cylinder wakes. Physics of Fluids, 8, 1, 1996.
1142:
Albarède, P., & Provansal, M. Quasi-periodic cylinder wakes and the
Ginzburg–Landau model. Journal of Fluid Mechanics, 291, 191-222, 1995.
148:
317:
1848:
1355:
649:
1816:
801:
1607:
1557:
1516:
1033:
1025:
610:
The same cylinder, now with a fin, suppressing the vortex street by reducing the region in which the side eddies can interact
443:
or the profile thickness, or some other given widths that are in fact stable design inputs; for flow channels usually the
2134:
1096:"Effects of Turbulence Model and Numerical Time Steps on von Karman Flow Behavior and Drag Accuracy of Circular Cylinder"
487:
of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears. Above the
1312:
Barkley, D.; Henderson, R.D. (1996). "Three-dimensional
Floquet stability analysis of the wake of a circular cylinder".
1474:
1238:
Jackson, C.P. (1987). "A finite-element study of the onset of vortex shedding in flow past variously shaped bodies".
1001:
1757:
2172:
1841:
936:
475:
of the fluid. For the wake of a circular cylinder, for which the reference length is conventionally the diameter
519:
1049:
Bayındır, Cihan; Namlı, Barış (2021). "Efficient sensing of von Kármán vortices using compressive sensing".
2114:
656:
70:
1834:
933: – Swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime
491:
value of 188.5, the flow becomes three-dimensional, with periodic variation along the cylinder. Above
674:
To prevent vortex shedding and mitigate the unwanted vibration of cylindrical bodies is the use of a
648:, especially when built together in clusters. Vortex shedding caused the collapse of three towers at
619:
659:
was originally attributed to excessive vibration due to vortex shedding, but was actually caused by
551:
954:
877:
62:
1948:
1587:
1793:
1773:
1496:
514:
lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding
232:
1537:
374:
403:
283:
2208:
930:
918:
868:(1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.
707:
464:
1436:
1385:
1321:
1247:
1194:
1107:
698:
97:
A look at the Kármán vortex street effect from ground level, as air flows quickly from the
66:
1120:
1095:
117:
A vortex street forms only at a certain range of flow velocities, specified by a range of
8:
2182:
2142:
1926:
1427:
Irwin, Peter A. (September 2010). "Vortices and tall buildings: A recipe for resonance".
905:
660:
472:
440:
308:
1440:
1389:
1325:
1251:
1198:
1111:
904:
In his autobiography, von Kármán described how his discovery was inspired by an
Italian
2120:
2020:
1857:
1563:
1409:
1337:
1263:
1215:
1184:
1172:
1125:
1076:
1058:
444:
261:
208:
23:
2154:
How Long Is the Coast of
Britain? Statistical Self-Similarity and Fractional Dimension
2203:
2147:
2047:
2042:
1983:
1973:
1911:
1724:
1603:
1567:
1553:
1512:
1452:
1413:
1401:
1267:
1220:
1129:
1080:
1029:
1021:
997:
675:
586:
428:
1341:
1072:
1998:
1714:
1595:
1545:
1504:
1444:
1393:
1329:
1294:
1255:
1210:
1202:
1115:
1068:
989:
865:
74:
960:
957: – Motions induced on bodies within a fluid flow due to vortices in the fluid
1921:
948:
942:
881:
861:
791:{\displaystyle {\text{St}}=0.198\left(1-{\frac {19.7}{{\text{Re}}_{d}}}\right)\ }
693:
535:
468:
118:
51:
47:
19:
1599:
885:
2109:
2104:
2037:
1701:
Mizota, Taketo; Zdravkovich, Mickey; Graw, Kai-U.; Leder, Alfred (March 2000).
1508:
909:
896:
527:
526:. It is this forced vibration that, at the correct frequency, causes suspended
439:
or a revolution body like a fuselage or a submarine, it is usually the profile
142:
31:
1785:
1769:
1549:
1333:
1259:
951: – Oscillating flow effect resulting from fluid passing over a blunt body
141:
in the flow of a fluid around a body or in a channel, and may be defined as a
2197:
2099:
2094:
1728:
1456:
1405:
1298:
645:
102:
98:
1958:
666:
Kármán turbulence is also a problem for airplanes, especially when landing.
510:
distribution. This means that the alternate shedding of vortices can create
2010:
1933:
1916:
1702:
1654:
Aerodynamics: Selected Topics in the Light of Their Historical Development
1224:
1206:
993:
690:
phenomenon to determine the optimal parameters for the tuned mass damper.
85:
2128:
2086:
2005:
1901:
1896:
981:
641:
496:
2075:
2070:
1988:
1891:
1544:, Chichester, UK: John Wiley & Sons, Ltd, p. 362, 2018-10-12,
1397:
634:
531:
436:
226:
109:
1691:
Von Kármán, T. (1954). Aerodynamics (Vol. 203). Columbus: McGraw-Hill.
1448:
1173:"Stability of two-dimensional potential flows using bicomplex numbers"
2177:
2080:
1826:
1719:
1594:, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. 1375–1392,
880:, he acknowledged that the vortex street had been studied earlier by
626:
623:
523:
515:
511:
138:
963: – Tendency of a fluid jet to stay attached to a convex surface
618:
vortices along object's sides can be highly undesirable, due to the
1906:
1871:
1189:
1063:
507:
503:
546:
93:
2032:
2027:
2015:
1993:
1978:
1886:
1797:
1777:
630:
463:
values varies with the size and shape of the body from which the
134:
1745:
1503:, Hoboken, NJ, USA: John Wiley & Sons, Inc., p. 1076,
1171:
Kleine, Vitor G.; Hanifi, Ardeshir; Henningson, Dan S. (2022).
484:
43:
1497:"Aerodynamic Sound Sources in Vehicles—Prediction and Control"
945: – Ratio of inertial to viscous forces acting on a liquid
2065:
1631:
Math. Phys. Klasse pp. 509–517 (1911) and pp. 547–556 (1912).
1586:
Crocker, Malcolm J. (2007-09-19), Crocker, Malcolm J. (ed.),
1283:"Bénard-von Kármán instability: transient and forced regimes"
913:
711:
55:
499:, vortex shedding becomes irregular and turbulence sets in.
451:(i.e. as usual in thin airfoil theory, one would employ the
1943:
1881:
1876:
726:
This formula generally holds true for the range 250 < Re
479:
of the circular cylinder, the lower limit of this range is
1700:
278:= a characteristic length parameter of the body or channel
133:) Reynolds number for a flow is a measure of the ratio of
1588:"Vibration Response of Structures to Fluid Flow and Wind"
1356:"Rapid Response - LANCE - Terra/MODIS 2010/226 14:55 UTC"
1495:
Ahmed, Syed R. (2007-09-19), Crocker, Malcolm J. (ed.),
195:{\displaystyle \mathrm {Re} _{L}={\frac {UL}{\nu _{0}}}}
550:
Kármán vortex street caused by wind flowing around the
145:
parameter of the global speed of the whole fluid flow:
1170:
361:{\displaystyle \nu _{0}={\frac {\mu _{0}}{\rho _{0}}}}
804:
738:
538:
on a car to vibrate more strongly at certain speeds.
406:
377:
320:
286:
264:
235:
211:
151:
1280:
61:
It is named after the engineer and fluid dynamicist
1093:
506:flow pattern forms around the body and changes the
311:
parameter of the fluid, which in turn is the ratio:
229:(i.e. the flow speed far from the fluid boundaries
830:
790:
419:
390:
360:
299:
270:
248:
217:
194:
2195:
1542:Noise and Vibration Control in Automotive Bodies
1311:
860:This dimensionless parameter St is known as the
65:, and is responsible for such phenomena as the "
1786:"Guadalupe Island Produces von Kármán Vortices"
1094:Amalia, E.; Moelyadi, M. A.; Ihsan, M. (2018).
917:century that can be found in the museum of the
1656:(Cornell University Press, Ithaca), pp. 68–69.
1842:
1665:A. Mallock, 1907: On the resistance of air.
1281:Provansal, M.; Mathis, C.; Boyer, L. (1987).
1048:
1796:from the original on 2021-12-22 – via
1776:from the original on 2021-12-22 – via
113:A vortex street in a 2D liquid of hard disks
1435:(9). American Institute of Physics: 68–69.
979:
831:{\displaystyle {\text{St}}={\frac {fd}{U}}}
1849:
1835:
1718:
1680:Comptes Rendus de l'Académie des Sciences
1214:
1188:
1119:
1062:
1682:(Paris), vol. 147, pp. 839–842, 970–972.
864:and is named after the Czech physicist,
692:
545:
108:
92:
84:
50:, which is responsible for the unsteady
18:
1592:Handbook of Noise and Vibration Control
1585:
1501:Handbook of Noise and Vibration Control
1237:
562:
2196:
1856:
1806:"Various Views of von Karman Vortices"
1375:
1044:
1042:
16:Repeating pattern of swirling vortices
1830:
1640:T. von Kármán: and H. Rubach, 1912:
1494:
1426:
1100:Journal of Physics: Conference Series
939: – Phenomenon of fluid mechanics
888:. Kármán tells the story in his book
42:) is a repeating pattern of swirling
1471:"Airport Opening Ceremony Postponed"
980:J.E. Cooper (2001). S. Braun (ed.).
2135:The Chemical Basis of Morphogenesis
1629:Nachr. Ges. Wissenschaft. Göttingen
1378:Meteorology and Atmospheric Physics
1039:
13:
522:of a body or structure, it causes
447:about which the fluid is flowing.
241:
157:
154:
14:
2220:
1738:
585:Simulated vortex street around a
541:
502:When a single vortex is shed, an
1957:
1744:
596:
571:
1694:
1685:
1672:
1659:
1646:
1634:
1621:
1579:
1530:
1488:
1463:
1420:
1369:
1348:
1305:
1274:
1121:10.1088/1742-6596/1005/1/012012
1073:10.1016/j.compfluid.2021.104975
46:, caused by a process known as
1642:Phys. Z.", vol. 13, pp. 49–59.
1231:
1164:
1155:
1145:
1136:
1087:
1010:
973:
657:original Tacoma Narrows Bridge
398:= the reference fluid density.
125:), typically above a limiting
1:
1358:. Rapidfire.sci.gsfc.nasa.gov
967:
1758:"von Karman vortex shedding"
937:Kelvin–Helmholtz instability
844:= vortex shedding frequency.
669:
7:
1762:Encyclopedia of Mathematics
1600:10.1002/9780470209707.ch116
924:
701:fitted to break up vortices
652:in 1965 during high winds.
650:Ferrybridge Power Station C
644:can be created in concrete
249:{\displaystyle U_{\infty }}
80:
10:
2225:
1509:10.1002/9780470209707.ch87
1314:Journal of Fluid Mechanics
1287:Journal of Fluid Mechanics
1240:Journal of Fluid Mechanics
871:
850:= diameter of the cylinder
721:
495:on the order of 10 at the
2165:
2115:D'Arcy Wentworth Thompson
2058:
1966:
1955:
1864:
1751:Von Kármán vortex streets
1550:10.1002/9781119515500.ch6
1334:10.1017/S0022112096002777
1260:10.1017/S0022112087002234
986:Encyclopedia of Vibration
620:vortex-induced vibrations
391:{\displaystyle \rho _{0}}
1299:10.1017/S002211208700223
955:Vortex-induced vibration
427:= the free stream fluid
420:{\displaystyle \mu _{0}}
300:{\displaystyle \nu _{0}}
129:value of about 90. The (
71:Ginzburg–Landau equation
40:von Kármán vortex street
589:cylindrical obstruction
1207:10.1098/rspa.2022.0165
1051:Computers & Fluids
1020:. McGraw-Hill (1963):
994:10.1006/rwvb.2001.0125
982:"Aeroelastic Response"
902:
832:
792:
702:
555:
552:Juan Fernández Islands
471:, as well as with the
421:
392:
362:
301:
272:
250:
219:
196:
114:
106:
90:
27:
1949:Widmanstätten pattern
1016:Theodore von Kármán,
931:Eddy (fluid dynamics)
894:
876:Although named after
833:
793:
696:
554:off the Chilean coast
549:
422:
393:
363:
302:
273:
251:
220:
197:
112:
96:
88:
58:around blunt bodies.
22:
1753:at Wikimedia Commons
1703:"Science in culture"
802:
736:
563:Engineering problems
404:
375:
318:
284:
262:
233:
209:
149:
36:Kármán vortex street
2183:Mathematics and art
2173:Pattern recognition
2143:Aristid Lindenmayer
1669:, A79, pp. 262–265.
1441:2010PhT....63i..68I
1390:1990MAP....43..145E
1326:1996JFM...322..215B
1252:1987JFM...182...23J
1199:2022RSPSA.47820165K
1112:2018JPhCS1005a2012A
988:. Elsevier: 87–97.
921:church in Bologna.
912:carrying the child
878:Theodore von Kármán
661:aeroelastic flutter
655:The failure of the
473:kinematic viscosity
309:kinematic viscosity
63:Theodore von Kármán
2121:On Growth and Form
2021:Logarithmic spiral
1858:Patterns in nature
1822:on March 12, 2016.
1678:H. Bénard, 1908:
1398:10.1007/BF01028117
828:
788:
703:
640:Even more serious
556:
534:to "sing" and the
518:is similar to the
445:hydraulic diameter
417:
388:
358:
307:= the free stream
297:
268:
246:
225:= the free stream
215:
192:
115:
107:
91:
75:bicomplex variable
52:separation of flow
28:
2191:
2190:
2148:Benoît Mandelbrot
2048:Self-organization
1984:Natural selection
1974:Pattern formation
1749:Media related to
1652:T. Kármán, 1954.
1609:978-0-470-20970-7
1559:978-1-119-51550-0
1518:978-0-470-20970-7
1449:10.1063/1.3490510
1034:978-0-486-43485-8
1026:978-0-07-067602-2
826:
808:
787:
778:
770:
742:
676:tuned mass damper
605:
580:
520:natural frequency
429:dynamic viscosity
356:
271:{\displaystyle L}
218:{\displaystyle U}
190:
73:, or by use of a
2216:
1999:Sexual selection
1961:
1851:
1844:
1837:
1828:
1827:
1823:
1821:
1815:. Archived from
1810:
1801:
1781:
1765:
1748:
1733:
1732:
1722:
1720:10.1038/35005158
1698:
1692:
1689:
1683:
1676:
1670:
1667:Proc. Royal Soc.
1663:
1657:
1650:
1644:
1638:
1632:
1627:T. von Kármán:
1625:
1619:
1618:
1617:
1616:
1583:
1577:
1576:
1575:
1574:
1534:
1528:
1527:
1526:
1525:
1492:
1486:
1485:
1483:
1482:
1473:. Archived from
1467:
1461:
1460:
1424:
1418:
1417:
1373:
1367:
1366:
1364:
1363:
1352:
1346:
1345:
1309:
1303:
1302:
1278:
1272:
1271:
1235:
1229:
1228:
1218:
1192:
1168:
1162:
1159:
1153:
1149:
1143:
1140:
1134:
1133:
1123:
1091:
1085:
1084:
1066:
1046:
1037:
1028:. Dover (1994):
1014:
1008:
1007:
977:
866:Vincenc Strouhal
856:= flow velocity.
837:
835:
834:
829:
827:
822:
814:
809:
806:
797:
795:
794:
789:
785:
784:
780:
779:
777:
776:
771:
768:
762:
743:
740:
607:
606:
582:
581:
426:
424:
423:
418:
416:
415:
397:
395:
394:
389:
387:
386:
367:
365:
364:
359:
357:
355:
354:
345:
344:
335:
330:
329:
306:
304:
303:
298:
296:
295:
277:
275:
274:
269:
255:
253:
252:
247:
245:
244:
224:
222:
221:
216:
201:
199:
198:
193:
191:
189:
188:
179:
171:
166:
165:
160:
119:Reynolds numbers
2224:
2223:
2219:
2218:
2217:
2215:
2214:
2213:
2194:
2193:
2192:
2187:
2161:
2054:
1962:
1953:
1860:
1855:
1819:
1808:
1804:
1784:
1768:
1756:
1741:
1736:
1699:
1695:
1690:
1686:
1677:
1673:
1664:
1660:
1651:
1647:
1639:
1635:
1626:
1622:
1614:
1612:
1610:
1584:
1580:
1572:
1570:
1560:
1536:
1535:
1531:
1523:
1521:
1519:
1493:
1489:
1480:
1478:
1469:
1468:
1464:
1425:
1421:
1374:
1370:
1361:
1359:
1354:
1353:
1349:
1310:
1306:
1279:
1275:
1236:
1232:
1177:Proc. R. Soc. A
1169:
1165:
1160:
1156:
1150:
1146:
1141:
1137:
1092:
1088:
1047:
1040:
1015:
1011:
1004:
978:
974:
970:
949:Vortex shedding
943:Reynolds number
927:
882:Arnulph Mallock
874:
862:Strouhal number
815:
813:
805:
803:
800:
799:
772:
767:
766:
761:
754:
750:
739:
737:
734:
733:
731:
724:
672:
615:
614:
613:
612:
611:
608:
597:
592:
591:
590:
583:
572:
565:
544:
411:
407:
405:
402:
401:
382:
378:
376:
373:
372:
350:
346:
340:
336:
334:
325:
321:
319:
316:
315:
291:
287:
285:
282:
281:
263:
260:
259:
240:
236:
234:
231:
230:
210:
207:
206:
184:
180:
172:
170:
161:
153:
152:
150:
147:
146:
83:
48:vortex shedding
17:
12:
11:
5:
2222:
2212:
2211:
2206:
2189:
2188:
2186:
2185:
2180:
2175:
2169:
2167:
2163:
2162:
2160:
2159:
2158:
2157:
2145:
2140:
2139:
2138:
2126:
2125:
2124:
2112:
2110:Wilson Bentley
2107:
2105:Joseph Plateau
2102:
2097:
2092:
2091:
2090:
2078:
2073:
2068:
2062:
2060:
2056:
2055:
2053:
2052:
2051:
2050:
2045:
2043:Plateau's laws
2040:
2038:Fluid dynamics
2035:
2025:
2024:
2023:
2018:
2013:
2003:
2002:
2001:
1996:
1991:
1986:
1976:
1970:
1968:
1964:
1963:
1956:
1954:
1952:
1951:
1946:
1941:
1936:
1931:
1930:
1929:
1924:
1919:
1914:
1904:
1899:
1894:
1889:
1884:
1879:
1874:
1868:
1866:
1862:
1861:
1854:
1853:
1846:
1839:
1831:
1825:
1824:
1802:
1790:NOAASatellites
1782:
1766:
1754:
1740:
1739:External links
1737:
1735:
1734:
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1684:
1671:
1658:
1645:
1633:
1620:
1608:
1578:
1558:
1529:
1517:
1487:
1462:
1419:
1384:(1): 145–151.
1368:
1347:
1304:
1273:
1230:
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1154:
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1038:
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1002:
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910:St Christopher
873:
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812:
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760:
757:
753:
749:
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720:
697:Chimneys with
671:
668:
646:cooling towers
629:to industrial
609:
595:
594:
593:
584:
570:
569:
568:
567:
566:
564:
561:
543:
542:In meteorology
540:
453:chord Reynolds
432:
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143:nondimensional
139:viscous forces
101:eastward over
82:
79:
32:fluid dynamics
15:
9:
6:
4:
3:
2:
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2118:
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2116:
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2111:
2108:
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2103:
2101:
2100:Ernst Haeckel
2098:
2096:
2095:Adolf Zeising
2093:
2089:
2088:
2084:
2083:
2082:
2079:
2077:
2074:
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2036:
2034:
2031:
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2029:
2026:
2022:
2019:
2017:
2014:
2012:
2009:
2008:
2007:
2004:
2000:
1997:
1995:
1992:
1990:
1987:
1985:
1982:
1981:
1980:
1977:
1975:
1972:
1971:
1969:
1965:
1960:
1950:
1947:
1945:
1942:
1940:
1939:Vortex street
1937:
1935:
1932:
1928:
1925:
1923:
1920:
1918:
1917:Quasicrystals
1915:
1913:
1910:
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1713:(6775): 226.
1712:
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1675:
1668:
1662:
1655:
1649:
1643:
1637:
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1611:
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1582:
1569:
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1533:
1520:
1514:
1510:
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1498:
1491:
1477:on 2016-07-26
1476:
1472:
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1458:
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1430:
1429:Physics Today
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1234:
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1174:
1167:
1158:
1148:
1139:
1131:
1127:
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1117:
1113:
1109:
1106:(1): 012012.
1105:
1101:
1097:
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1082:
1078:
1074:
1070:
1065:
1060:
1056:
1052:
1045:
1043:
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1031:
1027:
1023:
1019:
1013:
1005:
1003:9780122270857
999:
995:
991:
987:
983:
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972:
962:
961:Coandă effect
959:
956:
953:
950:
947:
944:
941:
938:
935:
932:
929:
928:
922:
920:
915:
911:
907:
901:
898:
893:
891:
887:
883:
879:
869:
867:
863:
855:
852:
849:
846:
843:
840:
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838:
823:
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816:
810:
781:
773:
763:
758:
755:
751:
747:
744:
732:< 200000:
730:
719:
716:
713:
709:
700:
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691:
687:
683:
679:
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667:
664:
662:
658:
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647:
643:
638:
636:
632:
628:
625:
621:
588:
560:
553:
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529:
525:
521:
517:
513:
509:
505:
500:
498:
494:
490:
486:
482:
478:
474:
470:
466:
462:
459:The range of
457:
454:
448:
446:
442:
438:
430:
412:
408:
400:
383:
379:
371:
370:
369:
351:
347:
341:
337:
331:
326:
322:
310:
292:
288:
280:
265:
258:
237:
228:
212:
205:
204:
203:
185:
181:
176:
173:
167:
162:
144:
140:
136:
132:
128:
124:
120:
111:
104:
103:Mojave Desert
100:
99:Pacific Ocean
95:
87:
78:
76:
72:
68:
64:
59:
57:
53:
49:
45:
41:
37:
33:
25:
24:Visualisation
21:
2209:Aerodynamics
2152:
2133:
2119:
2085:
2011:Chaos theory
1938:
1934:Tessellation
1817:the original
1812:
1789:
1761:
1710:
1706:
1696:
1687:
1679:
1674:
1666:
1661:
1653:
1648:
1641:
1636:
1628:
1623:
1613:, retrieved
1591:
1581:
1571:, retrieved
1541:
1538:"Wind Noise"
1532:
1522:, retrieved
1500:
1490:
1479:. Retrieved
1475:the original
1465:
1432:
1428:
1422:
1381:
1377:
1371:
1360:. Retrieved
1350:
1317:
1313:
1307:
1290:
1286:
1276:
1243:
1239:
1233:
1183:(20220165).
1180:
1176:
1166:
1157:
1147:
1138:
1103:
1099:
1089:
1054:
1050:
1018:Aerodynamics
1017:
1012:
985:
975:
919:San Domenico
903:
895:
890:Aerodynamics
889:
886:Henri Bénard
875:
859:
853:
847:
841:
728:
725:
717:
704:
688:
684:
680:
673:
665:
654:
639:
616:
557:
504:asymmetrical
501:
492:
488:
480:
476:
460:
458:
452:
449:
433:
314:
130:
126:
122:
116:
60:
39:
35:
29:
2129:Alan Turing
2087:Liber Abaci
2006:Mathematics
1912:in crystals
1902:Soap bubble
1897:Phyllotaxis
1320:: 215–241.
642:instability
635:skyscrapers
532:power lines
497:drag crisis
2198:Categories
2076:Empedocles
2071:Pythagoras
1989:Camouflage
1927:in biology
1922:in flowers
1892:Parastichy
1615:2023-08-11
1573:2023-08-11
1524:2023-08-11
1481:2016-10-18
1362:2013-12-20
1190:2203.05857
1064:2005.08325
1057:: 104975.
968:References
627:periscopes
437:bluff body
227:flow speed
2178:Emergence
2081:Fibonacci
1813:NASA page
1729:1476-4687
1568:240055532
1457:0031-9228
1414:122276209
1406:1436-5065
1268:123071463
1246:: 23–45.
1130:126372504
1081:234828962
759:−
670:Solutions
624:submarine
528:telephone
524:resonance
516:frequency
409:μ
380:ρ
368:between:
348:ρ
338:μ
323:ν
289:ν
242:∞
182:ν
2204:Vortices
1907:Symmetry
1865:Patterns
1794:Archived
1774:Archived
1342:53610776
1293:: 1–22.
1225:35702595
925:See also
906:painting
631:chimneys
512:periodic
508:pressure
135:inertial
81:Analysis
44:vortices
2166:Related
2033:Crystal
2028:Physics
2016:Fractal
1994:Mimicry
1979:Biology
1887:Meander
1798:YouTube
1778:YouTube
1437:Bibcode
1386:Bibcode
1322:Bibcode
1248:Bibcode
1216:9185835
1195:Bibcode
1108:Bibcode
897:Prandtl
872:History
798:where:
722:Formula
712:helical
699:strakes
587:no-slip
536:antenna
202:where:
67:singing
2059:People
1967:Causes
1727:
1707:Nature
1606:
1566:
1556:
1515:
1455:
1412:
1404:
1340:
1266:
1223:
1213:
1152:Turkey
1128:
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1024:
1000:
786:
708:eddies
485:energy
465:eddies
131:global
38:(or a
2066:Plato
1872:Crack
1820:(PDF)
1809:(PDF)
1564:S2CID
1410:S2CID
1338:S2CID
1264:S2CID
1185:arXiv
1126:S2CID
1077:S2CID
1059:arXiv
914:Jesus
748:0.198
441:chord
56:fluid
54:of a
1944:Wave
1882:Foam
1877:Dune
1725:ISSN
1604:ISBN
1554:ISBN
1513:ISBN
1453:ISSN
1402:ISSN
1221:PMID
1104:1005
1030:ISBN
1022:ISBN
998:ISBN
884:and
764:19.7
633:and
469:shed
467:are
34:, a
1715:doi
1711:404
1596:doi
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1505:doi
1445:doi
1394:doi
1330:doi
1318:322
1295:doi
1291:182
1256:doi
1244:182
1211:PMC
1203:doi
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530:or
489:Re
137:to
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
