Eddy (fluid dynamics)

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Downwind of obstacles, in this case, the Madeira and the Canary Islands off the west African coast, eddies create turbulent patterns called vortex streets.
When two currents (in this case the Oyashio and Kuroshio currents) collide, they create eddies. Phytoplankton become concentrated along the boundaries of these eddies, tracing out the motions of the water.

In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid flows past an obstacle.[1] The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind the obstacle flowing upstream, toward the back of the obstacle. This phenomenon is most visible behind large emergent rocks in swift-flowing rivers.

Another possible type of turbulence is the vortex. This notion is now applied to gases, which have the same properties as liquids. Here, no void is created, but only an area of lower pressure, but again, a backflow causes the gas to rotate.

Mesoscale ocean eddies[edit]

Eddies are common in the ocean, and range in diameter from centimeters to hundreds of kilometers. The smallest scale eddies may last for a matter of seconds, while the larger features may persist for months to years.

Eddies which are between about 10 and 500 km (6.2 and 310.7 miles) in diameter and persist for periods of days to months are known in oceanography as mesoscale eddies.[2]

Mesoscale eddies can be split into two categories: static eddies, caused by flow around an obstacle (see image), and transient eddies, caused by baroclinic instability.

When the ocean contains a sea surface height gradient this creates a jet or current, such as the Antarctic Circumpolar Current. This current as part of a baroclinically unstable system meanders and creates eddies (in much the same way as a meandering river forms an ox-bow lake). These types of mesoscale eddies have been observed in many of major ocean currents, including the Gulf Stream, the Agulhas Current, the Kuroshio Current, and the Antarctic Circumpolar Current, amongst others.

Mesoscale ocean eddies are characterized by currents which flow in a roughly circular motion around the center of the eddy. The sense of rotation of these currents may either be cyclonic or anticyclonic. Oceanic eddies are also usually made of water masses that are different from those outside of the eddy. That is, the water within an eddy usually has different temperature and salinity characteristics to the water outside of the eddy. There is a direct link between the water mass properties of an eddy and its rotation. Warm eddies rotate anti-cyclonically, while cold eddies rotate cyclonically.

Because eddies may have a vigorous circulation associated with them, they are of concern to naval and commercial operations at sea. Further, because eddies transport anomalously warm or cold water as they move, they have an important influence on heat transport in certain parts of the ocean.

Swirl and eddies in engineering[edit]

The propensity of a fluid to swirl is used to promote good fuel/air mixing in internal combustion engines.

A vortex street around a cylinder. This can occur around cylinders and spheres, for any fluid, cylinder size and fluid speed, provided that the flow has a Reynolds number in the range ~40 to ~1000.[3]

In fluid mechanics and transport phenomena, an eddy is not a property of the fluid, but a violent swirling motion caused by the position and direction of turbulent flow.[4]

Reynolds number and turbulence[edit]

Reynolds number is a unit-less number used to determine when turbulent flow will occur. Conceptually, the Reynolds number is the ratio between inertial forces and viscous forces.[5]

The general form for the Reynolds number flowing through a tube of radius r:


A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), turbulent flow, time-averaged (center), and turbulent flow, instantaneous depiction (right)

The transition from laminar to turbulent flow in a fluid is defined by the critical Reynolds number:

In terms of the critical Reynolds number, the critical velocity is represented as:

Schlieren photograph showing the thermal convection plume rising from an ordinary candle in still air. The plume is initially laminar, but transition to turbulence occurs in the upper 1/3 of the image. The image was made using the 1-meter-diameter schlieren mirror of Floviz Inc. by Dr. Gary Settles
Water flow observed in a pipe, as drawn by Osborne Reynolds in his best-known experiment on fluid dynamics in pipes. Water flows from left to right in the transparent tube, and dye (represented in black) flows in the middle. The nature of the flow (turbulent, laminar) can be observed easily. These drawings were published in Reynolds’ influential 1883 paper "An experimental investigation of the circumstances which determine whether the motion of water in parallel channels shall be direct or sinuous and of the law of resistance in parallel channels".

Research and development[edit]

A diagram showing the velocity distribution of a fluid moving through a circular pipe, for laminar flow (left), turbulent flow, time-averaged (center), and turbulent flow, instantaneous depiction (right)


Hemodynamics is the study of blood flow in the circulatory system. Blood flow in straight sections of the arterial tree are typically laminar (high, directed wall stress), but branches and curvatures in the system cause turbulent flow.[6] Turbulent flow in the arterial tree can cause a number of concerning effects, including atherosclerotic lesions, postsurgical neointimal hyperplasia, in-stent restenosis, vein bypass graft failure, transplant vasculopathy, and aortic valve calcification.

Industrial processes[edit]

Using turbulent flow to improve the properties of a golf ball in-flight

Lift and drag properties of golf balls are customized by the manipulation of dimples along the surface of the ball, allowing for the golf ball to travel further and faster in the air.[7]

Used to thoroughly mix fluids and increase reaction rates within industrial processes.

Fluid currents and pollution control[edit]

Oceanic and atmospheric currents transfer particles, debris, and organisms all across the globe. While the transport of organisms, such as phytoplankton, are essential for the preservation of ecosystems, oil and other pollutants are also mixed in the current flow and can carry pollution far from its origin.[8][9] Eddy formations circulate trash and other pollutants into concentrated areas which researchers are tracking to improve clean-up and pollution prevention.

Mesoscale ocean eddies play crucial rolls in transferring heat poleward, as well as maintaining heat gradients at different depths.[10]

Computational fluid dynamics[edit]

These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier-Stokes equations, are modelled by a linear constitutive relationship with the mean flow straining field, as:


  • is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
  • is the mean turbulent kinetic energy
  • is the mean strain rate
Note that that inclusion of in the linear constitutive relation is required by tensorial algebra purposes when solving for two-equation turbulence models (or any other turbulence model that solves a transport equation for .[11]

See also[edit]


  1. ^ Chiu, Jeng-Jiann; Chien, Shu (2011-01-01). "Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives". Physiological Reviews. 91 (1): 327–387. doi:10.1152/physrev.00047.2009. ISSN 0031-9333. PMC 3844671Freely accessible. PMID 21248169. 
  2. ^ Unseen Currents: A Blind Oceanographer Chases Undersea Storms at Popsci
  3. ^ Tansley, Claire E.; Marshall, David P. (2001). "Flow past a Cylinder on a Plane, with Application to Gulf Stream Separation and the Antarctic Circumpolar Current" (PDF). Journal of Physical Oceanography. 31 (11): 3274–3283. Bibcode:2001JPO....31.3274T. doi:10.1175/1520-0485(2001)031<3274:FPACOA>2.0.CO;2. 
  4. ^ Lightfoot, R. Byron Bird ; Warren E. Stewart ; Edwin N. (2002). Transport phenomena (2. ed.). New York, NY [u.a.]: Wiley. ISBN 0-471-41077-2. 
  5. ^ "Pressure". hyperphysics.phy-astr.gsu.edu. Retrieved 2017-02-12. 
  6. ^ Chiu, Jeng-Jiann; Chien, Shu (2011-01-01). "Effects of Disturbed Flow on Vascular Endothelium: Pathophysiological Basis and Clinical Perspectives". Physiological Reviews. 91 (1): 327–387. doi:10.1152/physrev.00047.2009. ISSN 0031-9333. PMC 3844671Freely accessible. PMID 21248169. 
  7. ^ "Why are Golf Balls Dimpled?". math.ucr.edu. Retrieved 2017-02-12. 
  8. ^ "https://www.sciencedaily.com/releases/2016/04/160419130133.htm". www.sciencedaily.com. Retrieved 2017-02-12.  External link in |title= (help)
  9. ^ "Ocean Pollution". National Oceanic and Atmospheric Administration. 
  10. ^ "Ocean Mesoscale Eddies – Geophysical Fluid Dynamics Laboratory". www.gfdl.noaa.gov. Retrieved 2017-02-12. 
  11. ^ "Linear eddy viscosity models -- CFD-Wiki, the free CFD reference". www.cfd-online.com. Retrieved 2017-02-12.