446:
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
911:
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.'
31:
705:
1970:
121:
558:
105:
80:" 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
1757:
584:
494:≈ 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
609:
445:
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
692:
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
466:
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
910:
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
628:
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
569:
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
700:
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
461:
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
927:
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
590:
588:
585:
589:
696:
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.
587:
615:
613:
610:
614:
467:
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.
725:
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.
1162:
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,
693:
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.
612:
2164:
807:
716:
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
267:
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.
1293:
211:
100:
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
377:
97:
586:
847:
729:
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.
633:
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
1816:
648:. For monitoring such engineering structures, the efficient measurements of von Kármán streets can be performed using smart sensing algorithms such as compressive sensing.
689:(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.
611:
265:
407:
746:
436:
316:
721:
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,
1481:
287:
234:
116:
mountains. This phenomenon observed from ground level is extremely rare, as most cloud-related Kármán vortex street activity is viewed from space.
1781:"Flow visualisation of the vortex shedding mechanism on circular cylinder using hydrogen bubbles illuminated by a laser sheet in a water channel"
1761:
1387:
Etling, D. (1990-03-01). "Mesoscale vortex shedding from large islands: A comparison with laboratory experiments of rotating stratified flows".
37:
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
570:
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).
1172:
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.
1153:
Albarède, P., & Provansal, M. Quasi-periodic cylinder wakes and the
Ginzburg–Landau model. Journal of Fluid Mechanics, 291, 191-222, 1995.
159:
17:
328:
1859:
1366:
660:
1827:
812:
1618:
1568:
1527:
1044:
1036:
621:
The same cylinder, now with a fin, suppressing the vortex street by reducing the region in which the side eddies can interact
454:
or the profile thickness, or some other given widths that are in fact stable design inputs; for flow channels usually the
2145:
1107:"Effects of Turbulence Model and Numerical Time Steps on von Karman Flow Behavior and Drag Accuracy of Circular Cylinder"
498:
of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears. Above the
1323:
Barkley, D.; Henderson, R.D. (1996). "Three-dimensional
Floquet stability analysis of the wake of a circular cylinder".
1485:
1249:
Jackson, C.P. (1987). "A finite-element study of the onset of vortex shedding in flow past variously shaped bodies".
1012:
1768:
2183:
1852:
947:
486:
of the fluid. For the wake of a circular cylinder, for which the reference length is conventionally the diameter
530:
1060:
Bayındır, Cihan; Namlı, Barış (2021). "Efficient sensing of von Kármán vortices using compressive sensing".
2125:
667:
81:
1845:
944: – Swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime
502:
value of 188.5, the flow becomes three-dimensional, with periodic variation along the cylinder. Above
685:
To prevent vortex shedding and mitigate the unwanted vibration of cylindrical bodies is the use of a
659:, especially when built together in clusters. Vortex shedding caused the collapse of three towers at
630:
670:
was originally attributed to excessive vibration due to vortex shedding, but was actually caused by
562:
965:
888:
73:
1959:
1598:
1804:
1784:
1507:
525:
lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding
243:
1548:
385:
414:
294:
2219:
941:
929:
879:(1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.
718:
475:
1447:
1396:
1332:
1258:
1205:
1118:
709:
108:
A look at the Kármán vortex street effect from ground level, as air flows quickly from the
77:
1131:
1106:
128:
A vortex street forms only at a certain range of flow velocities, specified by a range of
8:
2193:
2153:
1937:
1438:
Irwin, Peter A. (September 2010). "Vortices and tall buildings: A recipe for resonance".
916:
671:
483:
451:
319:
1451:
1400:
1336:
1262:
1209:
1122:
915:
In his autobiography, von Kármán described how his discovery was inspired by an
Italian
2131:
2031:
1868:
1574:
1420:
1348:
1274:
1226:
1195:
1183:
1136:
1087:
1069:
455:
272:
219:
34:
2165:
How Long Is the Coast of
Britain? Statistical Self-Similarity and Fractional Dimension
2214:
2158:
2058:
2053:
1994:
1984:
1922:
1735:
1614:
1578:
1564:
1523:
1463:
1424:
1412:
1278:
1231:
1140:
1091:
1040:
1032:
1008:
686:
597:
439:
1352:
1083:
2009:
1725:
1606:
1556:
1515:
1455:
1404:
1340:
1305:
1266:
1221:
1213:
1126:
1079:
1000:
876:
85:
971:
968: – Motions induced on bodies within a fluid flow due to vortices in the fluid
1932:
959:
953:
892:
872:
802:{\displaystyle {\text{St}}=0.198\left(1-{\frac {19.7}{{\text{Re}}_{d}}}\right)\ }
704:
546:
479:
129:
62:
58:
30:
1610:
896:
2120:
2115:
2048:
1712:
Mizota, Taketo; Zdravkovich, Mickey; Graw, Kai-U.; Leder, Alfred (March 2000).
1519:
920:
907:
538:
537:. It is this forced vibration that, at the correct frequency, causes suspended
450:
or a revolution body like a fuselage or a submarine, it is usually the profile
153:
42:
1796:
1780:
1560:
1344:
1270:
962: – Oscillating flow effect resulting from fluid passing over a blunt body
152:
in the flow of a fluid around a body or in a channel, and may be defined as a
2208:
2110:
2105:
1739:
1467:
1416:
1309:
656:
113:
109:
1969:
677:
Kármán turbulence is also a problem for airplanes, especially when landing.
521:
distribution. This means that the alternate shedding of vortices can create
2021:
1944:
1927:
1713:
1665:
Aerodynamics: Selected Topics in the Light of Their Historical Development
1235:
1217:
1004:
701:
phenomenon to determine the optimal parameters for the tuned mass damper.
96:
2139:
2097:
2016:
1912:
1907:
992:
652:
507:
2086:
2081:
1999:
1902:
1555:, Chichester, UK: John Wiley & Sons, Ltd, p. 362, 2018-10-12,
1408:
645:
542:
447:
237:
120:
1702:
Von Kármán, T. (1954). Aerodynamics (Vol. 203). Columbus: McGraw-Hill.
1459:
1184:"Stability of two-dimensional potential flows using bicomplex numbers"
2188:
2091:
1837:
1730:
1605:, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. 1375–1392,
891:, he acknowledged that the vortex street had been studied earlier by
637:
634:
534:
526:
522:
149:
974: – Tendency of a fluid jet to stay attached to a convex surface
629:
vortices along object's sides can be highly undesirable, due to the
1917:
1882:
1200:
1074:
518:
514:
557:
104:
2043:
2038:
2026:
2004:
1989:
1897:
1808:
1788:
641:
474:
values varies with the size and shape of the body from which the
145:
1756:
1514:, Hoboken, NJ, USA: John Wiley & Sons, Inc., p. 1076,
1182:
Kleine, Vitor G.; Hanifi, Ardeshir; Henningson, Dan S. (2022).
495:
54:
1508:"Aerodynamic Sound Sources in Vehicles—Prediction and Control"
956: – Ratio of inertial to viscous forces acting on a liquid
2076:
1642:
Math. Phys. Klasse pp. 509–517 (1911) and pp. 547–556 (1912).
1597:
Crocker, Malcolm J. (2007-09-19), Crocker, Malcolm J. (ed.),
1294:"Bénard-von Kármán instability: transient and forced regimes"
924:
722:
66:
510:, vortex shedding becomes irregular and turbulence sets in.
462:(i.e. as usual in thin airfoil theory, one would employ the
1954:
1892:
1887:
737:
This formula generally holds true for the range 250 < Re
490:
of the circular cylinder, the lower limit of this range is
1711:
289:= a characteristic length parameter of the body or channel
144:) Reynolds number for a flow is a measure of the ratio of
1599:"Vibration Response of Structures to Fluid Flow and Wind"
1367:"Rapid Response - LANCE - Terra/MODIS 2010/226 14:55 UTC"
1506:
Ahmed, Syed R. (2007-09-19), Crocker, Malcolm J. (ed.),
206:{\displaystyle \mathrm {Re} _{L}={\frac {UL}{\nu _{0}}}}
561:
Kármán vortex street caused by wind flowing around the
156:
parameter of the global speed of the whole fluid flow:
1181:
372:{\displaystyle \nu _{0}={\frac {\mu _{0}}{\rho _{0}}}}
815:
749:
549:
on a car to vibrate more strongly at certain speeds.
417:
388:
331:
297:
275:
246:
222:
162:
1291:
72:
It is named after the engineer and fluid dynamicist
1104:
517:flow pattern forms around the body and changes the
322:
parameter of the fluid, which in turn is the ratio:
240:(i.e. the flow speed far from the fluid boundaries
841:
801:
430:
401:
371:
310:
281:
259:
228:
205:
2206:
1553:Noise and Vibration Control in Automotive Bodies
1322:
871:This dimensionless parameter St is known as the
76:, and is responsible for such phenomena as the "
1797:"Guadalupe Island Produces von Kármán Vortices"
1105:Amalia, E.; Moelyadi, M. A.; Ihsan, M. (2018).
928:century that can be found in the museum of the
1667:(Cornell University Press, Ithaca), pp. 68–69.
1853:
1676:A. Mallock, 1907: On the resistance of air.
1292:Provansal, M.; Mathis, C.; Boyer, L. (1987).
1059:
1807:from the original on 2021-12-22 – via
1787:from the original on 2021-12-22 – via
124:A vortex street in a 2D liquid of hard disks
1446:(9). American Institute of Physics: 68–69.
990:
842:{\displaystyle {\text{St}}={\frac {fd}{U}}}
1860:
1846:
1729:
1691:Comptes Rendus de l'Académie des Sciences
1225:
1199:
1130:
1073:
1693:(Paris), vol. 147, pp. 839–842, 970–972.
875:and is named after the Czech physicist,
703:
556:
119:
103:
95:
61:, which is responsible for the unsteady
29:
1603:Handbook of Noise and Vibration Control
1596:
1512:Handbook of Noise and Vibration Control
1248:
573:
14:
2207:
1867:
1817:"Various Views of von Karman Vortices"
1386:
1055:
1053:
27:Repeating pattern of swirling vortices
1841:
1651:T. von Kármán: and H. Rubach, 1912:
1505:
1437:
1111:Journal of Physics: Conference Series
950: – Phenomenon of fluid mechanics
899:. Kármán tells the story in his book
53:) is a repeating pattern of swirling
1482:"Airport Opening Ceremony Postponed"
991:J.E. Cooper (2001). S. Braun (ed.).
2146:The Chemical Basis of Morphogenesis
1640:Nachr. Ges. Wissenschaft. Göttingen
1389:Meteorology and Atmospheric Physics
1050:
24:
533:of a body or structure, it causes
458:about which the fluid is flowing.
252:
168:
165:
25:
2231:
1749:
596:Simulated vortex street around a
552:
513:When a single vortex is shed, an
1968:
1755:
607:
582:
1705:
1696:
1683:
1670:
1657:
1645:
1632:
1590:
1541:
1499:
1474:
1431:
1380:
1359:
1316:
1285:
1132:10.1088/1742-6596/1005/1/012012
1084:10.1016/j.compfluid.2021.104975
57:, caused by a process known as
1653:Phys. Z.", vol. 13, pp. 49–59.
1242:
1175:
1166:
1156:
1147:
1098:
1021:
984:
668:original Tacoma Narrows Bridge
409:= the reference fluid density.
136:), typically above a limiting
13:
1:
1369:. Rapidfire.sci.gsfc.nasa.gov
978:
1769:"von Karman vortex shedding"
948:Kelvin–Helmholtz instability
855:= vortex shedding frequency.
680:
7:
1773:Encyclopedia of Mathematics
1611:10.1002/9780470209707.ch116
935:
712:fitted to break up vortices
663:in 1965 during high winds.
661:Ferrybridge Power Station C
655:can be created in concrete
260:{\displaystyle U_{\infty }}
91:
10:
2236:
1520:10.1002/9780470209707.ch87
1325:Journal of Fluid Mechanics
1298:Journal of Fluid Mechanics
1251:Journal of Fluid Mechanics
882:
861:= diameter of the cylinder
732:
506:on the order of 10 at the
2176:
2126:D'Arcy Wentworth Thompson
2069:
1977:
1966:
1875:
1762:Von Kármán vortex streets
1561:10.1002/9781119515500.ch6
1345:10.1017/S0022112096002777
1271:10.1017/S0022112087002234
997:Encyclopedia of Vibration
631:vortex-induced vibrations
402:{\displaystyle \rho _{0}}
1310:10.1017/S002211208700223
966:Vortex-induced vibration
438:= the free stream fluid
431:{\displaystyle \mu _{0}}
311:{\displaystyle \nu _{0}}
140:value of about 90. The (
82:Ginzburg–Landau equation
51:von Kármán vortex street
18:Von Kármán vortex street
600:cylindrical obstruction
1218:10.1098/rspa.2022.0165
1062:Computers & Fluids
1031:. McGraw-Hill (1963):
1005:10.1006/rwvb.2001.0125
993:"Aeroelastic Response"
913:
843:
803:
713:
566:
563:Juan Fernández Islands
482:, as well as with the
432:
403:
373:
312:
283:
261:
230:
207:
125:
117:
101:
38:
1960:Widmanstätten pattern
1027:Theodore von Kármán,
942:Eddy (fluid dynamics)
905:
887:Although named after
844:
804:
707:
565:off the Chilean coast
560:
433:
404:
374:
313:
284:
262:
231:
208:
123:
107:
99:
69:around blunt bodies.
33:
1764:at Wikimedia Commons
1714:"Science in culture"
813:
747:
574:Engineering problems
415:
386:
329:
295:
273:
244:
220:
160:
47:Kármán vortex street
2194:Mathematics and art
2184:Pattern recognition
2154:Aristid Lindenmayer
1680:, A79, pp. 262–265.
1452:2010PhT....63i..68I
1401:1990MAP....43..145E
1337:1996JFM...322..215B
1263:1987JFM...182...23J
1210:2022RSPSA.47820165K
1123:2018JPhCS1005a2012A
999:. Elsevier: 87–97.
932:church in Bologna.
923:carrying the child
889:Theodore von Kármán
672:aeroelastic flutter
666:The failure of the
484:kinematic viscosity
320:kinematic viscosity
74:Theodore von Kármán
2132:On Growth and Form
2032:Logarithmic spiral
1869:Patterns in nature
1833:on March 12, 2016.
1689:H. Bénard, 1908:
1409:10.1007/BF01028117
839:
799:
714:
651:Even more serious
567:
545:to "sing" and the
529:is similar to the
456:hydraulic diameter
428:
399:
369:
318:= the free stream
308:
279:
257:
236:= the free stream
226:
203:
126:
118:
102:
86:bicomplex variable
63:separation of flow
39:
2202:
2201:
2159:Benoît Mandelbrot
2059:Self-organization
1995:Natural selection
1985:Pattern formation
1760:Media related to
1663:T. Kármán, 1954.
1620:978-0-470-20970-7
1570:978-1-119-51550-0
1529:978-0-470-20970-7
1460:10.1063/1.3490510
1045:978-0-486-43485-8
1037:978-0-07-067602-2
837:
819:
798:
789:
781:
753:
687:tuned mass damper
616:
591:
531:natural frequency
440:dynamic viscosity
367:
282:{\displaystyle L}
229:{\displaystyle U}
201:
84:, or by use of a
16:(Redirected from
2227:
2010:Sexual selection
1972:
1862:
1855:
1848:
1839:
1838:
1834:
1832:
1826:. Archived from
1821:
1812:
1792:
1776:
1759:
1744:
1743:
1733:
1731:10.1038/35005158
1709:
1703:
1700:
1694:
1687:
1681:
1678:Proc. Royal Soc.
1674:
1668:
1661:
1655:
1649:
1643:
1638:T. von Kármán:
1636:
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1628:
1627:
1594:
1588:
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1586:
1585:
1545:
1539:
1538:
1537:
1536:
1503:
1497:
1496:
1494:
1493:
1484:. Archived from
1478:
1472:
1471:
1435:
1429:
1428:
1384:
1378:
1377:
1375:
1374:
1363:
1357:
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1314:
1313:
1289:
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1154:
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1145:
1144:
1134:
1102:
1096:
1095:
1077:
1057:
1048:
1039:. Dover (1994):
1025:
1019:
1018:
988:
877:Vincenc Strouhal
867:= flow velocity.
848:
846:
845:
840:
838:
833:
825:
820:
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808:
806:
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800:
796:
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773:
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618:
617:
593:
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437:
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434:
429:
427:
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408:
406:
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398:
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378:
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365:
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355:
346:
341:
340:
317:
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309:
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288:
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235:
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210:
209:
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200:
199:
190:
182:
177:
176:
171:
130:Reynolds numbers
21:
2235:
2234:
2230:
2229:
2228:
2226:
2225:
2224:
2205:
2204:
2203:
2198:
2172:
2065:
1973:
1964:
1871:
1866:
1830:
1819:
1815:
1795:
1779:
1767:
1752:
1747:
1710:
1706:
1701:
1697:
1688:
1684:
1675:
1671:
1662:
1658:
1650:
1646:
1637:
1633:
1625:
1623:
1621:
1595:
1591:
1583:
1581:
1571:
1547:
1546:
1542:
1534:
1532:
1530:
1504:
1500:
1491:
1489:
1480:
1479:
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1436:
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1188:Proc. R. Soc. A
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1103:
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1058:
1051:
1026:
1022:
1015:
989:
985:
981:
960:Vortex shedding
954:Reynolds number
938:
893:Arnulph Mallock
885:
873:Strouhal number
826:
824:
816:
814:
811:
810:
783:
778:
777:
772:
765:
761:
750:
748:
745:
744:
742:
735:
683:
626:
625:
624:
623:
622:
619:
608:
603:
602:
601:
594:
583:
576:
555:
422:
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383:
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221:
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195:
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183:
181:
172:
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94:
59:vortex shedding
28:
23:
22:
15:
12:
11:
5:
2233:
2223:
2222:
2217:
2200:
2199:
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2196:
2191:
2186:
2180:
2178:
2174:
2173:
2171:
2170:
2169:
2168:
2156:
2151:
2150:
2149:
2137:
2136:
2135:
2123:
2121:Wilson Bentley
2118:
2116:Joseph Plateau
2113:
2108:
2103:
2102:
2101:
2089:
2084:
2079:
2073:
2071:
2067:
2066:
2064:
2063:
2062:
2061:
2056:
2054:Plateau's laws
2051:
2049:Fluid dynamics
2046:
2036:
2035:
2034:
2029:
2024:
2014:
2013:
2012:
2007:
2002:
1997:
1987:
1981:
1979:
1975:
1974:
1967:
1965:
1963:
1962:
1957:
1952:
1947:
1942:
1941:
1940:
1935:
1930:
1925:
1915:
1910:
1905:
1900:
1895:
1890:
1885:
1879:
1877:
1873:
1872:
1865:
1864:
1857:
1850:
1842:
1836:
1835:
1813:
1801:NOAASatellites
1793:
1777:
1765:
1751:
1750:External links
1748:
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1395:(1): 145–151.
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921:St Christopher
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708:Chimneys with
682:
679:
657:cooling towers
640:to industrial
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554:
553:In meteorology
551:
464:chord Reynolds
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150:viscous forces
112:eastward over
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43:fluid dynamics
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2111:Ernst Haeckel
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2106:Adolf Zeising
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1950:Vortex street
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1928:Quasicrystals
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1488:on 2016-07-26
1487:
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1440:Physics Today
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1024:
1016:
1014:9780122270857
1010:
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1002:
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972:Coandă effect
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473:
470:The range of
468:
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453:
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411:
394:
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382:
381:
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362:
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114:Mojave Desert
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110:Pacific Ocean
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52:
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44:
36:
35:Visualisation
32:
19:
2220:Aerodynamics
2163:
2144:
2130:
2096:
2022:Chaos theory
1949:
1945:Tessellation
1828:the original
1823:
1800:
1772:
1721:
1717:
1707:
1698:
1690:
1685:
1677:
1672:
1664:
1659:
1652:
1647:
1639:
1634:
1624:, retrieved
1602:
1592:
1582:, retrieved
1552:
1549:"Wind Noise"
1543:
1533:, retrieved
1511:
1501:
1490:. Retrieved
1486:the original
1476:
1443:
1439:
1433:
1392:
1388:
1382:
1371:. Retrieved
1361:
1328:
1324:
1318:
1301:
1297:
1287:
1254:
1250:
1244:
1194:(20220165).
1191:
1187:
1177:
1168:
1158:
1149:
1114:
1110:
1100:
1065:
1061:
1029:Aerodynamics
1028:
1023:
996:
986:
930:San Domenico
914:
906:
901:Aerodynamics
900:
897:Henri Bénard
886:
870:
864:
858:
852:
739:
736:
728:
715:
699:
695:
691:
684:
676:
665:
650:
627:
568:
515:asymmetrical
512:
503:
499:
491:
487:
471:
469:
463:
460:
444:
325:
141:
137:
133:
127:
71:
50:
46:
40:
2140:Alan Turing
2098:Liber Abaci
2017:Mathematics
1923:in crystals
1913:Soap bubble
1908:Phyllotaxis
1331:: 215–241.
653:instability
646:skyscrapers
543:power lines
508:drag crisis
2209:Categories
2087:Empedocles
2082:Pythagoras
2000:Camouflage
1938:in biology
1933:in flowers
1903:Parastichy
1626:2023-08-11
1584:2023-08-11
1535:2023-08-11
1492:2016-10-18
1373:2013-12-20
1201:2203.05857
1075:2005.08325
1068:: 104975.
979:References
638:periscopes
448:bluff body
238:flow speed
2189:Emergence
2092:Fibonacci
1824:NASA page
1740:1476-4687
1579:240055532
1468:0031-9228
1425:122276209
1417:1436-5065
1279:123071463
1257:: 23–45.
1141:126372504
1092:234828962
770:−
681:Solutions
635:submarine
539:telephone
535:resonance
527:frequency
420:μ
391:ρ
379:between:
359:ρ
349:μ
334:ν
300:ν
253:∞
193:ν
2215:Vortices
1918:Symmetry
1876:Patterns
1805:Archived
1785:Archived
1353:53610776
1304:: 1–22.
1236:35702595
936:See also
917:painting
642:chimneys
523:periodic
519:pressure
146:inertial
92:Analysis
55:vortices
2177:Related
2044:Crystal
2039:Physics
2027:Fractal
2005:Mimicry
1990:Biology
1898:Meander
1809:YouTube
1789:YouTube
1448:Bibcode
1397:Bibcode
1333:Bibcode
1259:Bibcode
1227:9185835
1206:Bibcode
1119:Bibcode
908:Prandtl
883:History
809:where:
733:Formula
723:helical
710:strakes
598:no-slip
547:antenna
213:where:
78:singing
2070:People
1978:Causes
1738:
1718:Nature
1617:
1577:
1567:
1526:
1466:
1423:
1415:
1351:
1277:
1234:
1224:
1163:Turkey
1139:
1090:
1043:
1035:
1011:
797:
719:eddies
496:energy
476:eddies
142:global
49:(or a
2077:Plato
1883:Crack
1831:(PDF)
1820:(PDF)
1575:S2CID
1421:S2CID
1349:S2CID
1275:S2CID
1196:arXiv
1137:S2CID
1088:S2CID
1070:arXiv
925:Jesus
759:0.198
452:chord
67:fluid
65:of a
1955:Wave
1893:Foam
1888:Dune
1736:ISSN
1615:ISBN
1565:ISBN
1524:ISBN
1464:ISSN
1413:ISSN
1232:PMID
1115:1005
1041:ISBN
1033:ISBN
1009:ISBN
895:and
775:19.7
644:and
480:shed
478:are
45:, a
1726:doi
1722:404
1607:doi
1557:doi
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1456:doi
1405:doi
1341:doi
1329:322
1306:doi
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1267:doi
1255:182
1222:PMC
1214:doi
1192:478
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1080:doi
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541:or
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148:to
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