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Encyclopedia > Turbulence
 Turbulent flow around an obstacle; the flow further upstream is laminar Laminar and turbulent water flow over the hull of a submarine Turbulence in the tip vortex from an airplane wing

## Contents

Consider the flow of water over a simple smooth object, such as a sphere. At very low speeds the flow is laminar, i.e., the flow is smooth (though it may involve vortices on a large scale). As the speed increases, at some point the transition is made to turbulent ("chaotic") flow. In turbulent flow, unsteady vortices appear on many scales and interact with each other. Drag due to boundary layer skin friction increases. The structure and location of boundary layer separation often changes, sometimes resulting in a reduction of overall drag. Because laminar-turbulent transition is governed by Reynolds number, the same transition occurs if the size of the object is gradually increased, or the viscosity of the fluid is decreased, or if the density of the fluid is increased. A sphere is a perfectly symmetrical geometrical object. ... A plot of the trajectory Lorenz system for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. ... An object falling through a gas or liquid experiences a force in direction opposite to its motion. ... In physics and fluid mechanics, the boundary layer is that layer of fluid in the immediate vicinity of a bounding surface. ... In fluid mechanics, the Reynolds number is the ratio of inertial forces (vsÏ) to viscous forces (Î¼/L) and consequently it quantifies the relative importance of these two types of forces for given flow conditions. ... The related Category:Units of viscosity has been nominated for deletion, merging, or renaming. ... In physics, density is defined as mass m per unit volume V. For the common case of a homogeneous substance, it is expressed as: where, in SI units: Ï (rho) is the density of the substance, measured in kgÂ·m-3 m is the mass of the substance, measured in kg...

Turbulence causes the formation of eddies of many different length scales. Most of the kinetic energy of the turbulent motion is contained in the large scale structures. The energy "cascades" from these large scale structures to smaller scale structures by an inertial and essentially inviscid mechanism. This process continues, creating smaller and smaller structures which produces a hierarchy of eddies. Eventually this process creates structures that are small enough that molecular diffusion becomes important and viscous dissipation of energy finally takes place. The scale at which this happens is the Kolmogorov length scale. There are very few or no other articles that link to this one. ...

Turbulent diffusion is usually described by a turbulent diffusion coefficient. This turbulent diffusion coefficient is defined in a phenomenological sense, by analogy with the molecular diffusivities, but it does not have a true physical meaning, being dependent on the flow conditions, and not a property of the fluid, itself. In addition, the turbulent diffusivity concept assumes a constitutive relation between a turbulent flux and the gradient of a mean variable similar to the relation between flux and gradient that exists for molecular transport. In the best case, this assumption is only an approximation. Nevertheless, the turbulent diffusivity is the simplest approach for quantitative analysis of turbulent flows, and many models have been postulated to calculate it. For instance, in large bodies of water like oceans this coefficient can be found using Richardson's four-third power law and is governed by the random walk principle. In rivers and large ocean currents, the diffusion coefficient is given by variations of Elder's formula. The Diffusion Coefficient is given by where D is the diffusion coefficient in dimensions of [length2 time-1] T is the temperature in dimensions of Kelvin R is the gas constant in dimensions of [energy temperature-1 parts-1] See also Ficks law of diffusion Categories: Science stubs ... Lewis Fry Richardson (October 11, 1881 - September 30, 1953) was a mathematician, physicist and psychologist. ... In mathematics, computer science, and physics, a random walk, sometimes called a drunkards walk, is a formalisation of the intuitive idea of taking successive steps, each in a random direction. ...

When designing piping systems, turbulent flow requires a higher input of energy from a pump (or fan) than laminar flow. However, for applications such as heat exchangers and reaction vessels, turbulent flow is essential for good heat transfer and mixing.

### Examples of turbulence

• Smoke rising from a cigarette. For the first few centimetres it remains laminar, and then becomes unstable and turbulent. Similarly, the dispersion of pollutants in the atmosphere is governed by turbulent processes.
• Flow over a golf ball. (This can be best understood by considering the golf ball to be stationary, with air flowing over it.) If the golf ball were smooth, the boundary layer flow over the front of the sphere would be laminar at typical conditions. However, the boundary layer would separate early, as the pressure gradient switched from favorable (pressure decreasing in the flow direction) to unfavorable (pressure increasing in the flow direction), creating a large region of low pressure behind the ball that creates high form drag. To prevent this from happening, the surface is dimpled to perturb the boundary layer and promote transition to turbulence. This results in higher skin friction, but moves the point of boundary layer separation further along, resulting in lower form drag and lower overall drag.
• The mixing of warm and cold air in the atmosphere by wind, which causes Clear-air turbulence experienced during airplane flight, as well as poor astronomical seeing (the blurring of images seen through the atmosphere.)
• Most of the terrestrial atmospheric circulation
• The oceanic and atmospheric mixed layers and intense oceanic currents.
• The flow conditions in many industrial equipment (such as pipes, ducts, precipitators, gas scrubbers, etc.) and machines (for instance, internal combustion engines and gas turbines).
• The external flow over all kind of vehicles such as cars, airplanes, ships and submarines.
• The motions of matter in stellar atmospheres.
• A jet exhausting from a nozzle into a quiescent fluid. As the flow emerges into this external fluid, shear layers originating at the lips of the nozzle are created. These layers separate the fast moving jet from the external fluid, and at a certain critical Reynolds number they become unstable and break down to turbulence.
Unsolved problems in physics: Is it possible to make a theoretical model to describe the behavior of a turbulent flow — in particular, its internal structures?
For the Hyundai Tiburon Turbulence car, see Hyundai Tiburon
For the film of the same name, see Turbulence (film)
For the record label, see Turbulence Records

Smoke from a wildfire Smoke is a suspension in air (aerosol) of small particles resulting from incomplete combustion of a fuel. ... A smoking symbol. ... Atmospheric dispersion modeling is performed with computer programs that use mathematical equations and algorithms to simulate how pollutants in the ambient atmosphere disperse in the atmosphere. ... A golf ball on a tee with a driver ready for a drive A golf ball is a ball designed for use in the game of golf. ... In aerodynamics, form drag, profile drag, or pressure drag, is a component of parasitic drag. ... Clear-Air Turbulence (often abbreviated CAT and sometimes colloquially referred to as air pockets) is the erratic movement of air masses in the absence of any visual cues (such as clouds). ... Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... The oceanic or limnological mixed layer is the top zone in the ocean or a lake, having variable depth depending on how far the energy from the wind has penetrated into the water. ... Image File history File links No higher resolution available. ... This is a list of some of the unsolved problems in physics. ... The Hyundai Tiburon is a compact coupe produced by Hyundai since 1996. ... Turbulence is a 1997 film directed by Robert Butler which stars Ray Liotta and Lauren Holly. ... Turbulence Records is a trance music record label based in Portsmouth, UK. It began its life back in 2005 with the release of See The Light by Paradise (who also remix regularly for the labels other releases). ...

Schematic diagram illustrating how optical wavefronts from a distant star may be perturbed by a turbulent layer in the atmosphere. ... Atmospheric dispersion modeling is performed with computer programs that use mathematical equations and algorithms to simulate how pollutants in the ambient atmosphere disperse in the atmosphere. ... A plot of the trajectory Lorenz system for values r = 28, Ïƒ = 10, b = 8/3 In mathematics and physics, chaos theory describes the behavior of certain nonlinear dynamical systems that under certain conditions exhibit a phenomenon known as chaos. ... Clear-Air Turbulence (often abbreviated CAT and sometimes colloquially referred to as air pockets) is the erratic movement of air masses in the absence of any visual cues (such as clouds). ... A downdraft is downward moving air, usually the direct result of air convection within the thunderstorm. ... Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ... The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations that describe the motion of fluid substances such as liquids and gases. ... The Darcy-Weisbach equation is an important and widely used equation in hydraulics. ... The Poiseuilles law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow Î¦V of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant... It has been suggested that this article or section be merged into Supercell. ... The Reynolds number is the most important dimensionless number in fluid dynamics and provides a criterion for determining dynamic similitude. ... Swing bowling is a technique used for bowling in the sport of cricket. ... Velocimetry is the measurement of the velocity of fluids, as often used to solve fluid dynamics problems, or to study fluid networks, as well as in industrial and process control applications, or in the creation of new kinds of fluid flow sensors. ... Vortex created by the passage of an aircraft wing, revealed by coloured smoke A vortex (pl. ... 1967 Model Cessna 182K in flight showing after-market vortex generators on the wing leading edge A vortex generator is an aerodynamic surface, basically a small vane, that creates a vortex. ... Wake turbulence, also known as jetwash, is turbulence that forms behind an aircraft as it passes through the air. ... Wingtip vortices stream from an F-15E as it disengages from a KC-10 Extender following midair refueling. ... NASA wind tunnel with the model of a plane A wind tunnel is a research tool developed to assist with studying the effects of air moving over or around solid objects. ...

## References

1. ^ http://www.weizmann.ac.il/home/fnfal/KRSPhysTodayApr2006.pdf
2. ^ http://www.eng.auburn.edu/users/thurobs/Turb.html Turbulence
3. ^ http://www.fortunecity.com/emachines/e11/86/fluid.html Turbulent Times for Fluids

1a. Falkovich, Gregory and Sreenivasan, Katepalli R., "Lessons from hydrodynamic turbulence," Physics Today, vol. 59, no. 4, pages 43 - 49 (April 2006). See: http://www.phy.olemiss.edu/~jgladden/phys510/spring06/turbulence.pdf

U. Frisch, "Turbulence: The Legacy of A. N. Kolmogorov" (Cambridge University Press 1995) http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521457132

T. Bohr, M.H. Jensen, G. Paladin and A.Vulpiani, "Dynamical Systems Approach to Turbulence" (Cambridge University Press 1998) http://www.cambridge.org/catalogue/catalogue.asp?isbn=9780521475143

Original scientific research papers:

(1) Kolmogorov, Andrey Nikolaevich, "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers," Doklady Akademii Nauk SSSR [Proceedings of the Academy of Sciences of the USSR], Vol. 30, pages 299 - 303 (1941).

Republished in English in:

(1a) Kolmogorov, Andrey Nikolaevich, "The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers," Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 434, No. 1890, pages 9 - 13 (8 July 1991).

(2) Kolmogorov, Andrey Nikolaevich, "Dissipation of energy in locally isotropic turbulence," Doklady Akademii Nauk SSSR [Proceedings of the Academy of Sciences of the USSR], Vol. 32, pages 16 - 18 (1941).

Republished in English in:

(2a) Kolmogorov, Andrey Nikolaevich, "Dissipation of energy in locally isotropic turbulence," Proceedings of the Royal Society of London, Series A: Mathematical and Physical Sciences, Vol. 434, No. 1890, pages 15 - 17 (8 July 1991).

Biographies of Andrey Nikolaevich Kolmogorov (1903 - 1987):

University of St. Andrews, Scotland: http://www-history.mcs.st-andrews.ac.uk/Biographies/Kolmogorov.html

Results from FactBites:

 Turbulence - Wikipedia, the free encyclopedia (739 words) In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by random, stochastic property changes. The statistical description of turbulent flow was suggested by the Russian mathematician Andrey Kolmogorov, this description is known to be approximate at best. Turbulence causes the formation of eddies which are defined by the Kolmogorov length scale and a turbulent diffusion coefficient.
 Safer air travel - Turbulence (702 words) Turbulence is the leading cause of in-flight injuries. In-flight turbulence is the leading cause of injuries to passengers and crew. Occupants injured during turbulence are usually not wearing seatbelts, ignoring recommendations to keep seatbelts fastened even when the signs are not illuminated.
More results at FactBites »

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