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[[Image:Vortex-street-animation.gif|thumb|400px|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.]]
== Michael Kors Melbourne What Youre Not to Read ==
In [[fluid dynamics]], a '''Kármán vortex street''' (or a '''von Kármán vortex sheet''') is a repeating pattern of swirling [[vortex|vortices]] caused by the unsteady [[flow separation|separation of flow]] of a [[fluid]] around blunt bodies. It is named after the engineer and fluid dynamicist [[Theodore von Kármán]],<ref>Theodore von Kármán, ''Aerodynamics''. McGraw-Hill (1963): ISBN 978-0-07-067602-2. Dover (1994): ISBN 978-0-486-43485-8.</ref> and is responsible for such phenomena as the "[[conductor gallop#Flutter|singing]]" of suspended telephone or power lines, and the vibration of a car antenna at certain speeds.


==Analysis==
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[[Image:Vortex-street-1.jpg|thumb|Kármán vortex street caused by wind flowing around the [[Juan Fernández Islands]] off the Chilean coast.]]
 
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A vortex street will only form at a certain range of flow velocities, specified by a range of [[Reynolds number]]s (''Re''), typically above a limiting ''Re'' value of about 90. The Reynolds number is a measure of the ratio of [[inertia]]l to [[viscosity|viscous forces]] in the flow of a fluid and may be defined as:
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:<math>\mathrm{Re}=\frac{Vd}{\nu}\ </math>
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*<math>d</math> = the diameter of the cylinder (or some other suitable measure of width of non-circular bodies) about which the fluid is flowing.
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*<math>V</math> = the steady [[velocity]] of the flow upstream of the cylinder.
 
*<math>\nu\,</math> = the [[Kinematic viscosity|kinematic viscosity]] of the fluid.
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:<math>\mathrm{Re}=\frac{\rho _\infty V _\infty d }{\mu _\infty} </math>
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*<math>\rho _\infty</math>  = the free stream fluid density.
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*<math>V _\infty</math>  = the steady free stream velocity of the flow upstream of the cylinder.
 
*<math>d</math>    = the diameter of the cylinder (or some other suitable measure of width of non-circular bodies) about which the fluid is flowing.
  </ul>
*<math>\mu _\infty</math> = the free stream [[dynamic viscosity]] of the fluid.
 
The range of ''Re'' values will vary with the size and shape of the body from which the [[Eddy (fluid dynamics)|eddies]] are being [[Vortex shedding|shed]], as well as with the [[kinematic viscosity]] of the fluid. Over a large ''Re'' range (47<Re<10<sup>5</sup> for circular cylinders) eddies are shed continuously from each side of the body, 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 [[energy]] of the vortices is consumed by viscosity as they move further down stream, and the regular pattern disappears.
 
When a single vortex is shed, an [[Symmetry|asymmetrical]] flow pattern forms around the body and changes the [[pressure]] distribution. This means that the alternate shedding of vortices can create [[Frequency|periodic]] lateral (sideways) forces on the body in question, causing it to vibrate. If the vortex shedding [[frequency]] is similar to the [[Fundamental frequency#Mechanical systems|natural frequency]] of a body or structure, it causes [[resonance]]. It is this forced vibration that, at the correct frequency, causes suspended [[telephone line|telephone]] or [[power line]]s to "sing" and the [[antenna (radio)|antenna]] on a car to vibrate more strongly at certain speeds.
{{clear}}
 
==In meteorology==
{{Expand section|date=November 2012}}
 
===Observations of mountains and islands known to cause a Kármán vortex street===
Winds blowing past isolated islands or mountains that project into the atmosphere can cause a huge vortex street disturbance downwind of them, visible in satellite photographs such as the gallery below.  The following is a list of islands and mountains worldwide known to cause the Von Kármán vortex street.
[[File:Prapiroon Oct 18 2012 2.10 UTC.jpg|thumb|230px|right|A Kármán vortex street off Jeju Do (left), caused by the downward windflow of [[2012 Pacific typhoon season#Typhoon Prapiroon (Nina)|Typhoon Prapiroon]] on the east.]]
*[[Guadalupe Island]] – known to cause the Von Kármán vortices, usually in May–September. It is an active island in generating the phenomenon, with a vortex street appearing almost every day in June to August.<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=987 |title=Atmospheric Vortices near Guadalupe Island : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Hallasan]] Volcano, [[Jeju Province|Jeju Island]], [[South Korea]] –Known to cause one of the world's largest  Von Karman vortex streets, every winter, usually starting from October to April.<ref>{{cite web|url=http://www.hko.gov.hk/wxinfo/intersat/satellite_gallery/misc_e.htm#m6 |title=Miscellaneous |publisher=Hko.gov.hk |date= |accessdate=2013-12-20}}</ref>
*[[Yakushima|Yakushima Island]], Japan.<ref>{{cite web|url=http://www.eorc.jaxa.jp/en/imgdata/topics/2005/tp050307.html |title=Seen from Space - Striped Clouds Crossing over the Sea of Japan |publisher=EORC |date= |accessdate=2013-12-20}}</ref>
*[[Socorro Island]], a small volcanic island in the [[Revillagigedo Islands]], a possession of [[Mexico]] – the small, 37.4&nbsp;km<sup>2</sup> island often causes long, small vortex streets downwind.<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=1254 |title=Swirls of Lace : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Juan Fernández Islands|Juan Fernandez Islands]]<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=625 |title=Landsat 7 Reveals Large-scale Fractal Motion of Clouds : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*All [[Canary Islands]]<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=AtlanticOcean.A2010226.1455.1km.jpg |title=Rapid Response - LANCE - Terra/MODIS 2010/226 14:55 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Madeira Island]] <ref>{{cite web|url=http://visibleearth.nasa.gov/view.php?id=63391 |title=NASA Visible Earth: Vortex street near Madeira Island |publisher=Visibleearth.nasa.gov |date= |accessdate=2013-12-20}}</ref>
* Most of [[Cape Verde Islands]]<ref>http://eoimages.gsfc.nasa.gov/images/imagerecords/72000/72646/CapeVerde.A2005005.1225.250m.jpg</ref>
*[[Beerenberg]] Volcano, [[Jan Mayen]] island.<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=2270 |title=A Vortex Street in the Arctic : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Herald Island (Arctic)|Herald Island]], [[Russia]] – with only 364 meters height, the small, 11.3&nbsp;km<sup>2</sup> island is one of the smallest known to cause a vortex street every summer visible in the low [[fog]].<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=9043 |title=Wrangel Island, Russia : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Saint Helena|Saint Helena Island]]<ref>{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=79720 |title=Cloud Vortices off St. Helena : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Broutona|Broutona Island]], [[Russia]].<ref name="Image of the Day">{{cite web|url=http://earthobservatory.nasa.gov/IOTD/view.php?id=2313 |title=Von Karman Vortices over Broutona : Image of the Day |publisher=Earthobservatory.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Chyornie Bratya|Chyornie Bratya islands]], [[Russia]]<ref name="Image of the Day"/>
*[[Zavodovski Island|Zavodovski volcano]] [[Atlantic Ocean|South Atlantic Ocean]].
*[[Tristan da Cunha]], South Atlantic ocean.<ref>http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi</ref>
*[[South Georgia and the South Sandwich Islands|Southern Sandwich Islands]]<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=SouthSandwich.A2012118.1620.1km.jpg |title=Rapid Response - LANCE - Terra/MODIS 2012/118 16:20 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Aleutian Islands]], [[Alaska]] – about 70% of the group of islands are known to create Von Kármán vortex streets.<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=AleutianIslands.A2012108.2240.500m.jpg |title=Rapid Response - LANCE - Terra/MODIS 2012/108 22:40 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Heard Island and McDonald Islands|Heard Island]], south [[Indian Ocean]]<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=HeardIsland.A2011262.0430.1km.jpg |title=Rapid Response - LANCE - Terra/MODIS 2011/262 04:30 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Galápagos Islands|Galapagos Islands]]<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=Galapagos.A2010251.1635.1km.jpg |title=Rapid Response - LANCE - Terra/MODIS 2010/251 16:35 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Juan Fernández Islands]], [[Chile]]<ref>{{cite web|url=http://rapidfire.sci.gsfc.nasa.gov/cgi-bin/imagery/single.cgi?image=JuanFernandezIslands.A2010020.1920.1km.jpg |title=Rapid Response - LANCE - Terra/MODIS 2010/020 19:20 UTC |publisher=Rapidfire.sci.gsfc.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Rishiri Island]], Japan.<ref>{{cite web|author=Čeština |url=http://en.wikipedia.org/wiki/Rishiri_Island |title=Rishiri Island - Wikipedia, the free encyclopedia |publisher=En.wikipedia.org |date= |accessdate=2013-12-20}}</ref>
*[[Crozet Islands]], Southern Indian Ocean<ref>{{cite web|url=http://visibleearth.nasa.gov/view.php?id=72574 |title=NASA Visible Earth: Cloud vortices off the Crozet Islands, south Indian Ocean |publisher=Visibleearth.nasa.gov |date= |accessdate=2013-12-20}}</ref>
*[[Kuril Islands]], about 75% of the islands exhibit a vortex street, usually in the summer from June to August under low fog.The vortices don't form in winter, even through the same clouds are around due to the fast movement off winds caused by [[extratropical cyclone]]s.<ref>{{cite web|url=http://www.masterfile.com/stock-photography/image/679-02682151/Von-Karman-vortices.-Coloured-composite-satellite-image-of-clouds-forming-von-Karman |title=Von Karman vortices. Coloured composite satellite image of clouds forming von Karman vortices, an effect that occurs when an object disturbs the flow of a fluid, leading to the creation of a chain of spiral eddies (a vortex street). In this case, the objects causing vortex streets to form are islands in the Kuril Islands chain between Russia and Japan. The effect occurs at all scales and it is imp - Stock Photos |publisher=Masterfile.com |date= |accessdate=2013-12-20}}</ref>
* [[Jan Mayen]], Northern Atlantic Ocean.<ref>http://earthobservatory.nasa.gov/NaturalHazards/view.php?id=77654</ref>
 
==Engineering problems==
[[File:Karman Vortex Street Off Cylinder.ogv|thumb|400px|Simulated vortex street around a [[No slip condition|no-slip]] cylindrical obstruction.]]
[[File:Vortex.fin.small.ogv|thumb|400px|The same cylinder, now with a fin, suppressing the vortex street by reducing the region in which the side eddies can interact.]]
 
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 prevents the formation of coherent vortices.<ref>{{cite journal|title=Vortices and tall buildings: A recipe for resonance|first=Peter A. | last=Irwin|journal=Physics Today|date=September 2010|pages=68–69|volume=63|number=9|ISSN=0031-9228|publisher=American Institute of Physics}}</ref> Periodic crosswind forces set up by vortices along object's sides can be highly undesirable, and hence it is important for engineers to account for the possible effects of vortex shedding when designing a wide range of structures, from [[submarine]] [[periscope]]s to industrial [[chimney]]s and [[skyscraper]]s.
 
In order to prevent the unwanted vibration of such cylindrical bodies, a longitudinal fin can be fitted on the downstream side, which, providing it is longer than the diameter of the cylinder, will prevent the eddies 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, [[helix|helical]] projections that look like 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. Another countermeasure with tall buildings is using variation in the diameter with height, such as tapering - that prevents the entire building being driven at the same frequency.
 
Even more serious [[instability]] can be created in concrete [[cooling tower]]s, for example, especially when built together in clusters. Vortex shedding caused the collapse of three towers at [[Ferrybridge power stations#Construction|Ferrybridge Power Station C]] in 1965 during high winds.
 
The failure of the [[Tacoma Narrows Bridge (1940)]]  was originally attributed to excessive vibration due to vortex shedding, but was actually caused by  [[aeroelastic flutter]].
{{clear}}
[[File:Proserpine Mill - January 2012.jpg|thumb|Chimneys with spirals outside to break up vortices.]]
 
==Formula==
:<math>\frac{fd}{V}=0.198\left (1-\frac{19.7}{Re}\right )\ </math>
 
where:
 
*''f'' = vortex shedding frequency.
*''d'' = diameter of the cylinder
*''V'' = flow velocity.
 
This formula will generally hold true for the range 250 < Re < 2 × 10<sup>5</sup>.  The dimensionless parameter ''fd/V'' is known as the [[Strouhal number]] and is named after the Czech physicist, [[Vincenc Strouhal]] (1850–1922) who first investigated the steady humming or singing of telegraph wires in 1878.
 
==Insect flight==
Recent studies have shown that [[insects]] such as [[bee]]s borrow energy from the [[Turbulence|vortices]] that form around their wings during flight. Vortices inherently create [[drag (physics)|drag]]. Insects can recapture some of this energy and use it to improve speed and maneuverability:  They rotate their wings before starting the return stroke, and the wings are lifted by the [[Eddy (fluid dynamics)|eddies]] of air created on the downstroke.  The high frequency oscillation of insect wings means that many hundreds of vortices are shed every second.  However, this leads to a symmetric vortex street pattern, unlike the ones shown above.
 
== History ==
 
Although named after [[Theodore von Kármán]],<ref>T. von Kármán:  ''Nachr. Ges. Wissenschaft. Göttingen'' Math. Phys. Klasse pp. 509&ndash;517 (1911) and pp. 547&ndash;556 (1912).</ref><ref>T. von Kármán: and H. Rubach, 1912:  ''Phys. Z.", vol. 13, pp. 49&ndash;59.</ref> he acknowledged<ref>T. Kármán, 1954.  ''Aerodynamics:  Selected Topics in the Light of Their Historical Development'' (Cornell University Press, Ithaca), pp. 68&ndash;69.</ref> that the vortex street had been studied earlier by [[Arnulph Mallock|Mallock]]<ref>A. Mallock, 1907:  On the resistance of air.  ''Proc. Royal Soc.'', A79, pp. 262&ndash;265.</ref> and [[Henri Bénard|Bénard]].<ref>H. Bénard, 1908:  ''Comptes rendus de l'Académie des Sciences'' (Paris), vol. 147, pp. 839&ndash;842, 970&ndash;972.</ref>
 
==See also==
*[[Kelvin–Helmholtz instability]]
* [[Vortex shedding]]
* [[Vortex-induced vibration]]
* [[Coandă effect]]
 
==References==
<references/>
 
== External links ==
{{commons category|Von Kármán vortex streets}}
* [http://www.encyclopediaofmath.org/index.php/Von_K%C3%A1rm%C3%A1n_vortex_shedding Encyclopedia of Mathematics article on von Karman vortex shedding]
* [http://www.youtube.com/watch?v=GmTmDM7jHzA 3D animation of the Vortex Flow Measuring Principle]
* [http://www.enseeiht.fr/hmf/travaux/CD0102/travaux/optmfn/gpfmho/01-02/grp1/presenta.htm Vortex streets and Strouhal instability]
* [http://www.sciam.com/article.cfm?articleID=000DF125-5545-1C75-9B81809EC588EF21 How Insects Fly] (which can produce von Kármán vortices)
* [http://www.youtube.com/watch?v=_AJgEa2dbJU YouTube] — Flow visualisation of the vortex shedding mechanism on circular cylinder using hydrogen bubbles illuminated by a laser sheet in a water channel
* [http://disc.sci.gsfc.nasa.gov/oceancolor/additional/science-focus/ocean-color/science_focus.shtml/vonKarman_vortices.shtml Various Views of von Karman Vortices], NASA page
 
{{DEFAULTSORT:Karman Vortex Street}}
[[Category:Vortices]]
[[Category:Aerodynamics]]

Latest revision as of 18:16, 11 December 2014

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