# Turbulence

views updated May 18 2018

# Turbulence

Historical overview

The Reynolds number

Formation of eddies

Resources

Turbulence is the formation of eddies in a fluid (liquid or gas). It is produced whenever a fluid (under certain conditions) is in contact with a solid and there is relative motion between them. For example, turbulence occurs when wind flows past a building or past a mountain; when the ocean flows past an island; when a baseball flies by a batter; when a jet airplane moves in the stratosphere; or when a river flows past a bridge pier. In all these cases, eddies form behind the obstacle (i.e., downstream), and eventually are carried away by the main body of fluid.

## Historical overview

Turbulence has long been observed, but its scientific study began with the work of Scottish engineer and physicist William John Macquorn Rankine (182072). Later, British fluid dynamics engineer Osborne Reynolds (18421912) defined the number bearing his name, and German physicist Ludwig Prandtl (18751953) put forth the limiting-layer hypothesis.

Today, the study of turbulence, experimental and theoretical, continues; but an agreement between both approaches is still in the future.

## The Reynolds number

There is a numbercalled the Reynolds numberwhose values indicate clearly whether the motion of a fluid in a certain region is turbulent or not. It is defined as:

Whether an obstacle carries any eddies, and whether these are released into the flow downstream depends upon the speed of the incoming fluid, the size of the obstacle, and the internal friction (viscosity) of the fluid, according to Professor Karen J. Heywood (of the School of Environmental Sciences, University of East Anglia, United Kingdom), writing in Physics Education. Just like a solid body, a parcel of liquid or gas has mass, and therefore inertia. Inertial force is the amount of force required to stop a body that is moving along steadily with its own inertia. For example, the force to stop a charging rhinoceros moving toward a person would be greater than that needed to stop a hummingbird at the same speed. The inertial force necessary to stop a parcel of water that occupies a unit volume (1 m3) is proportional to the square of its speed (v2) divided by a length typical of the obstacle (d)for example, the diameter of a stone in a river. All fluids, as they flow, present friction between their different parts. This property is called viscosity. Liquids are more viscous than gases, and, among liquids, corn syrup is much more viscous than water. The viscous force (internal friction) working on an object of diameter d moving through a fluid at speed v is proportional to h.d/d 2, where h is the viscosity coefficient of the fluid. Dividing the expression for the inertial force by that for the frictional force, one obtains R as given by the above equation.

## Formation of eddies

If one places an obstacle, e.g., a sphere, at rest in the midst of a fluid stream, physical intuition suggests that the part of the fluid that is really in contact with the obstacle must be at rest. However, photographs taken in different laboratories appeared not to support this idea. In order to explain what was happening, German physicist Ludwig Prandtl introduced the hypothesis of the limiting layer, according to which in the immediate neighborhood of the obstacle there is a very thin layer of fluid whose velocity parallel to the surface of the object grows very rapidly, from zero at the surface itself to the velocity of the main body of fluid far from the object. This limiting layer is very thin upstream, but broadens downstream, i.e., behind the obstacle.

Inside the downstream limit layer the fluid begins to move backward and in circles, until the eddies form when the Reynolds number is R = 5. As the fluid velocity grows, bringing R to a value of 70, the limit

### KEY TERMS

Fluid A piece of matter that flows; i.e., is deformed under the action of even the weakest forces.

Inertia The tendency of an object in motion to remain in motion, and the tendency of an object at rest to remain at rest.

Viscosity The internal friction within a fluid that makes it resist flow.

layer broadens still more downstream, forming what is called a von Karman vortex street, after Hungarian-American engineer and physicist Theodore von Karman (18811963). These eddies finally leave the vicinity of the obstacle and float away with the main fluid current. If R keeps increasing to values of between 1,000 and 2,500, eddies become more frequent and the vortex street broadens still more, finally breaking up and forming a turbulent wake. At this stage, the motion of fluid particles is chaotic and varies in time.

## Resources

### BOOKS

Cannon, John, and Bhimsen Shivamoggi, eds. Mathematical and Physical Theory of Turbulence. Boca Raton, FL: Chapman & Hall/CRC, 2006.

Cebeci, Tuncer. Analysis of Turbulent Flows.
Amsterdam, Netherlands, and Oxford, UK: Elsevier, 2004.

Peinke, J., et al., eds. Progress in Turbulence. Berlin, Germany, and New York: Springer, 2005.

Tsinober, Arkady. An Informal Introduction to Turbulence.
Dordrecht, Germany, and Boston, MA: Kluwer Academic Publishers, 2001.

### PERIODICALS

Heywood, Karen J. Fluid flows in the environment: an introduction. 1993. Phys. Educ. 2843-47 doi:10.1088/0031-9120/28/1/008.

Raul A. Simon

# Turbulence

views updated Jun 27 2018

# Turbulence

Turbulence is the formation of eddies in a fluid (liquid or gas). It is produced whenever a fluid (under certain conditions) is in contact with a solid and there is relative motion between them; for example: when wind flows past a building or past a mountain; when the ocean flows past an island ; when a baseball flies by; when a jet plane moves in the stratosphere; or when a river flows past a bridge pier. In all these cases, eddies form behind the obstacle (i.e., "downstream"), and eventually are carried away by the main body of fluid.

## Historical overview

Turbulence has long been observed, but its scientific study began with the work of William John Macquorn Rankine (1820-1872); later, Osborne Reynolds (1842-1912) defined the number bearing his name, and Ludwig Prandtl (1875-1953) put forth the limiting-layer hypothesis.

Today, the study of turbulence, experimental and theoretical, continues; but an agreement between both approaches is still in the future.

## The Reynolds number

There is a number—called Reynolds number—whose values indicate clearly whether the motion of a fluid in a certain region is turbulent or not. It is defined as:

Whether an obstacle carries any eddies, and whether these are released into the flow downstream depends upon the speed of the incoming fluid, the size of the obstacle and the internal friction (viscosity ) of the fluid, according to Karen J. Heywood writing in Physics Education. Just like a solid body, a parcel of liquid or gas has mass, and therefore inertia. Inertial force is the amount of force required to stop a body that is moving along steadily with its own inertia (for example, the force to stop a charging rhino moving towards you would be greater than that needed to stop a hummingbird at the same speed). The inertial force necessary to stop a parcel of water that occupies a unit volume (1 m3, say) is proportional to the square of its speed (v2) divided by a length typical of the obstacle (d)—say, the diameter of a stone in a river. All fluids, as they flow, present friction between their different parts. This property is called viscosity. Liquids are more viscous than gases, and, among liquids, corn syrup is much more viscous than water. The viscous force (internal friction) working on an object of diameter d moving through a fluid at speed v is proportional to h.d/d 2, where h is the viscosity coefficient of the fluid. Dividing the expression for the inertial force by that for the frictional force, we obtain R as given by the above equation.

## Formation of eddies

If we place an obstacle, e.g., a sphere , at rest in the midst of a fluid stream, our physical intuition suggests

that the part of the fluid which is really in contact with the obstacle must be at rest. However, photographs taken in different laboratories appeared not to support this idea. In order to explain what was happening, Ludwig Prandtl (1875-1953) introduced the hypothesis of the "limiting layer," according to which in the immediate neighborhood of the obstacle there is a very thin layer of fluid whose velocity parallel to the surface of the object brows very rapidly, from zero at the surface itself to the velocity of the main body of fluid far from the object. This limiting layer is very thin upstream, but broadens downstream, i.e., behind the obstacle.

Inside the downstream limit layer the fluid begins to move backwards and in circles, until the eddies form when the Reynolds number is R = 5. As the fluid velocity grows, bringing R to a value of 70, the limit layer broadens still more downstream, forming what is called a "von Karman vortex street" after Theodor von Karman (born 1881). These eddies finally leave the vicinity of the obstacle and float away with the main fluid current. If R keeps increasing to values of 1000 or 2500, eddies become more frequent and the vortex street broadens still more, finally breaking up and forming a "turbulent wake." At this stage the motion of fluid particles is chaotic and varies in time .

## Resources

### periodicals

Heywood, Karen J. "Fluid Flows in the Environment: An Introduction." Physics Education 28 (1993): 43.

Simon, R.A. "La Hidrodinamica." Charlas de Fisica 9 (1992): 43.

Raul A. Simon

## KEY TERMS

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Fluid

—A piece of matter that flows; i.e., is deformed under the action of even the weakest forces.

Inertia

—The tendency of an object in motion to remain in motion, and the tendency of an object at rest to remain at rest.

Viscosity

—The internal friction within a fluid that makes it resist flow.

# Turbulence

views updated Jun 27 2018

# Turbulence ★½ 1996 (R)

When you fly, it's usually the turbulence that makes you throw up. Well, this movie isn't that bad, but you may experience a touch of nausea. Flight attendant Teri (Holly) is pushing the drink cart on a strangely vacant New York to L.A. Christmas Eve run. Among the passengers are convicted felons Ryan (Liotta) and Stubbs (Gleeson), who are either on their way to a more secure prison or fulfilling the “consumption of airline food” portion of their sentence. The prisoners seize a gun from the marshals and accidentally rub out the cockpit crew. With all the passengers locked away, Teri must battle the serial rapist/killer Ryan as well as learn to fly the plane through a horrible storm. Passengers on the left of the screen may look out and see “Passenger 57,” while those on the right can see the ancient monument of “Airport 75.” 103m/C VHS, DVD . Ray Liotta, Lauren Holly, Hector Elizondo, Brendan Gleeson, Ben Cross, Rachel Ticotin, Jeffrey DeMunn, John Finn, Catherine Hicks; D: Robert Butler; W: Jonathan Brett; C: Lloyd Ahern II; M: Shirley Walker.

# turbulence

views updated May 23 2018

tur·bu·lence / ˈtərbyələns/ • n. violent or unsteady movement of air or water, or of some other fluid: the plane shuddered as it entered some turbulence. ∎ fig. conflict; confusion: a time of political turbulence.

# turbulence

views updated May 08 2018

turbulence Disturbed flow in a moving stream of air. It is manifested by variations of wind speed and direction (including vertical components), by vertical exchanges of mass, heat, momentum, water vapour, and any pollutants present, caused by eddies.