# Eddy (fluid dynamics)

In fluid dynamics, an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime.[2] 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 naturally observed behind large emergent rocks in swift-flowing rivers.

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.[1]

## Swirl and eddies in engineering

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

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.[3]

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)

## Reynolds number and turbulence

In 1883, scientist Osborne Reynolds conducted a fluid dynamics experiment involving water and dye, where he adjusted the velocities of the fluids and observed the transition from laminar to turbulent flow, characterized by the formation of eddies and vortices.[4] Turbulent flow is defined as the flow in which the system's inertial forces are dominant over the viscous forces. This phenomenon is described by Reynolds number, 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 (or diameter d):

Reynolds Experiment (1883). Osborne Reynolds standing beside his apparatus.

${\displaystyle Re={2v\rho r \over \mu }={\rho vd \over \mu }}$

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

where: ${\displaystyle {v}=velocity}$

${\displaystyle \rho =density}$

${\displaystyle r=radius}$

${\displaystyle \mu =viscosity}$

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

${\displaystyle Re_{c}\approx 2000}$

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

${\displaystyle v_{c}={R_{c}\mu \over \rho d}}$

## Research and development

### Hemodynamics

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.[2] 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.

Comparison of air flow around a smooth golf ball versus a dimpled golf ball.

### Industrial processes

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.[6][7]

The data from turbulent-flow phenomena has been used to model different transitions in fluid flow regimes, which are used to thoroughly mix fluids and increase reaction rates within industrial processes.[8]

### Fluid currents and pollution control

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.[9][10] 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 roles in transferring heat poleward, as well as maintaining heat gradients at different depths.[11]

### Computational fluid dynamics

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:

${\displaystyle -\rho \langle u_{i}u_{j}\rangle =2\mu _{t}S_{i,j}-{2 \over 3}\rho \kappa \delta _{i,j}}$

where

• ${\displaystyle \mu _{t}}$ is the coefficient termed turbulence "viscosity" (also called the eddy viscosity)
• ${\displaystyle \kappa ={\tfrac {1}{2}}(\langle u_{1}u_{1}\rangle +\langle u_{2}u_{2}\rangle +\langle u_{3}u_{3}\rangle )}$ is the mean turbulent kinetic energy
• ${\displaystyle S_{i,j}}$ is the mean strain rate
Note that that inclusion of ${\displaystyle {\tfrac {2}{3}}\rho \kappa \delta _{i,j}}$ 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 ${\displaystyle \kappa }$ .[12]

## Mesoscale ocean eddies

Downwind of obstacles, in this case, the Madeira and the Canary Islands off the west African coast, eddies create turbulent patterns called vortex streets.

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 that 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.[13]

Mesoscale eddies can be split into two categories: static eddies, caused by flow around an obstacle (see animation), 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 that 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 (such as Haida Eddies). Oceanic eddies are also usually made of water masses that are different from those outside the eddy. That is, the water within an eddy usually has different temperature and salinity characteristics to the water outside 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.

## References

1. ^ 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.
2. ^ a b 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 3844671. PMID 21248169.
3. ^ 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.
4. ^ Kambe, Tsutomu (2007). Elementary Fluid Mechanics. World Scientific Publishing Co. Pte. Ltd. p. 240. ISBN 978-981-256-416-0.
5. ^ "Pressure". hyperphysics.phy-astr.gsu.edu. Retrieved 2017-02-12.
6. ^ Arnold, Douglas. "The Flight of a Golf Ball" (PDF).
7. ^ "Why are Golf Balls Dimpled?". math.ucr.edu. Retrieved 2017-02-12.
8. ^ Dimotakis, Paul. "The Mixing Transition in Turbulent Flows" (PDF). California Institute of Technology Information Tech Services.
9. ^ "Ocean currents push phytoplankton, and pollution, around the globe faster than thought". Science Daily. 16 April 2016. Retrieved 2017-02-12.
10. ^ "Ocean Pollution". National Oceanic and Atmospheric Administration.
11. ^ "Ocean Mesoscale Eddies – Geophysical Fluid Dynamics Laboratory". www.gfdl.noaa.gov. Retrieved 2017-02-12.
12. ^ "Linear eddy viscosity models -- CFD-Wiki, the free CFD reference". www.cfd-online.com. Retrieved 2017-02-12.
13. ^ https://journals.ametsoc.org/doi/pdf/10.1175/1520-0485%282001%29031%3C3274%3AFPACOA%3E2.0.CO%3B2
Beaufort Gyre

The Beaufort Gyre is a wind-driven ocean current located in the Arctic Ocean polar region. The gyre contains both ice and water. It accumulates fresh water by the process of melting the ice floating on the surface of the water.

Eddy covariance

The eddy covariance (also known as eddy correlation and eddy flux) technique is a key atmospheric measurement technique to measure and calculate vertical turbulent fluxes within atmospheric boundary layers. The method analyzes high-frequency wind and scalar atmospheric data series, and yields values of fluxes of these properties. It is a statistical method used in meteorology and other applications (micrometeorology, oceanography, hydrology, agricultural sciences, industrial and regulatory applications, etc.) to determine exchange rates of trace gases over natural ecosystems and agricultural fields, and to quantify gas emissions rates from other land and water areas. It is frequently used to estimate momentum, heat, water vapour, carbon dioxide and methane fluxes.The technique is also used extensively for verification and tuning of global climate models, mesoscale and weather models, complex biogeochemical and ecological models, and remote sensing estimates from satellites and aircraft. The technique is mathematically complex, and requires significant care in setting up and processing data. To date, there is no uniform terminology or a single methodology for the Eddy Covariance technique, but much effort is being made by flux measurement networks (e.g., FluxNet, Ameriflux, ICOS, CarboEurope, Fluxnet Canada, OzFlux, NEON, and iLEAPS) to unify the various approaches.

The technique has additionally proven applicable under water to the benthic zone for measuring oxygen fluxes between seafloor and overlying water. In these environments, the technique is generally known as the eddy correlation technique, or just eddy correlation. Oxygen fluxes are extracted from raw measurements largely following the same principles as used in the atmosphere, and they are typically used as a proxy for carbon exchange, which is important for local and global carbon budgets. For most benthic ecosystems, eddy correlation is the most accurate technique for measuring in-situ fluxes. The technique's development and its applications under water remains a fruitful area of research.

Index of physics articles (E)

The index of physics articles is split into multiple pages due to its size.

Index of wave articles

This is a list of Wave topics.

Kármán vortex street

In fluid dynamics, a Kármán vortex street (or a von Kármán vortex street) is a repeating pattern of swirling vortices, caused by a process known as vortex shedding, which is responsible for the unsteady separation of flow of a fluid around blunt bodies. It is named after the engineer and fluid dynamicist Theodore von Kármán, and is responsible for such phenomena as the "singing" of suspended telephone or power lines and the vibration of a car antenna at certain speeds.

Lorenz Magaard

Lorenz Magaard (born May 21, 1934 in Wallsbüll, Germany) is a German-American mathematician and oceanographer. He made essential contributions to the theory of ocean waves and earned particular credit for organizing education and research.

Ocean gyre

In oceanography, a gyre () is any large system of circulating ocean currents, particularly those involved with large wind movements. Gyres are caused by the Coriolis effect; planetary vorticity along with horizontal and vertical friction, determine the circulation patterns from the wind stress curl (torque).The term gyre can be used to refer to any type of vortex in the air or the sea, even one that is man-made, but it is most commonly used in oceanography to refer to the major ocean systems.

Ocean surface topography

Ocean surface topography or sea surface topography, also called dynamic topography, are highs and lows on the ocean surface, similar to the hills and valleys of Earth's land surface depicted on a topographic map.

These variations are expressed in terms of sea surface height (SSH) relative to the Earth's geoid.

The main purpose of measuring ocean surface topography is to understand the large-scale circulation of the ocean.

Wake turbulence

Wake turbulence is a disturbance in the atmosphere that forms behind an aircraft as it passes through the air. It includes various components, the most important of which are wingtip vortices and jetwash. Jetwash refers simply to the rapidly moving gases expelled from a jet engine; it is extremely turbulent, but of short duration. Wingtip vortices, on the other hand, are much more stable and can remain in the air for up to three minutes after the passage of an aircraft. It is therefore not true turbulence in the aerodynamic sense, as this would be chaotic. Instead, it refers to the similarity to atmospheric turbulence as experienced by an aircraft flying through this region of disturbed air.

Wingtip vortices occur when a wing is generating lift. Air from below the wing is drawn around the wingtip into the region above the wing by the lower pressure above the wing, causing a vortex to trail from each wingtip. The strength of wingtip vortices is determined primarily by the weight and airspeed of the aircraft. Wingtip vortices make up the primary and most dangerous component of wake turbulence.

Wake turbulence is especially hazardous in the region behind an aircraft in the takeoff or landing phases of flight. During take-off and landing, aircraft operate at high angle of attack. This flight attitude maximizes the formation of strong vortices. In the vicinity of an airport there can be multiple aircraft, all operating at low speed and low altitude, and this provides extra risk of wake turbulence with reduced height from which to recover from any upset.

Whirlpool

A whirlpool is a body of rotating water produced by opposing currents or a current running into an obstacle. Small whirlpools form when a bath or a sink is draining. More powerful ones in seas or oceans may be termed maelstroms. Vortex is the proper term for a whirlpool that has a downdraft.In narrow ocean straits with fast flowing water, whirlpools are often caused by tides. Many stories tell of ships being sucked into a maelstrom, although only smaller craft are actually in danger. Smaller whirlpools appear at river rapid and can be observed downstream of manmade structures such as weirs and dams. Large cataracts, such as Niagara Falls, produce strong whirlpools.

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