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For other uses, see Turbulence (disambiguation).


Turbulence is commonly observed in everyday phenomena such as surf, fast flowing rivers, billowing storm clouds, or smoke from a chimney, and most fluid flows occurring in nature and created in engineering applications are turbulent.[2][3]:2 Turbulence is caused by excessive kinetic energy in parts of a fluid flow, which overcomes the dampening effect of the fluid's viscosity. For this reason turbulence is easier to create in low viscosity fluids, but more difficult in highly viscous fluids. In general terms, in turbulent flow, unsteady vortices appear of many sizes which interact with each other, consequently drag due to friction effects increases. This would increase the energy needed to pump fluid through a pipe, for instance. However this effect can also be exploited by such as aerodynamic spoilers on aircraft, which deliberately "spoil" the laminar flow to increase drag and reduce lift.

The onset of turbulence can be predicted by a dimensionless constant called the Reynolds number, which calculates the balance between kinetic energy and viscous damping in a fluid flow. However, turbulence has long resisted detailed physical analysis, and the interactions within turbulence creates a very complex situation. Richard Feynman has described turbulence as the most important unsolved problem of classical physics.[4]

Examples of turbulence[edit]

Turbulence in the tip vortex from an airplane wing
  • Most of the terrestrial atmospheric circulation
  • The oceanic and atmospheric mixed layers and intense oceanic currents.
  • The motions of matter in stellar atmospheres.
  • Biologically generated turbulence resulting from swimming animals affects ocean mixing.[5]
Question dropshade.png Unsolved problem in physics:
(more unsolved problems in physics)
  • Recently, turbulence in porous media became a highly debated subject.[8]



Turbulence is characterized by the following features:





Integral length scales 
Kolmogorov length scales 
Taylor microscales 



A more detailed presentation of turbulence with emphasis on high-Reynolds number flow, intended for a general readership of physicists and applied mathematicians, is found in the Scholarpedia articles by Benzi and Frisch[13] and by Falkovich.[14]

There are many scales of meteorological motions; in this context turbulence affects small-scale motions.[15]

Onset of turbulence[edit]

The plume from this candle flame goes from laminar to turbulent. The Reynolds number can be used to predict where this transition will take place

The onset of turbulence can be predicted by the Reynolds number, which is the ratio of inertial forces to viscous forces within a fluid which is subject to relative internal movement due to different fluid velocities, in what is known as a boundary layer in the case of a bounding surface such as the interior of a pipe. A similar effect is created by the introduction of a stream of higher velocity fluid, such as the hot gases from a flame in air. This relative movement generates fluid friction, which is a factor in developing turbulent flow. Counteracting this effect is the viscosity of the fluid, which as it increases, progressively inhibits turbulence, as more kinetic energy is absorbed by a more viscous fluid. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions, and is a guide to when turbulent flow will occur in a particular situation.[16]

This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems, and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full size version. Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed. A flow situation in which the kinetic energy is significantly absorbed due to the action of fluid molecular viscosity gives rise to a laminar flow regime. For this the dimensionless quantity the Reynolds number (Re) is used as a guide.

With respect to laminar and turbulent flow regimes:


The Reynolds number is defined as[17]


  • ρ is the density of the fluid (SI units: kg/m3)
  • v is a characteristic velocity of the fluid with respect to the object (m/s)
  • L is a characteristic linear dimension (m)
  • μ is the dynamic viscosity of the fluid (Pa·s or N·s/m2 or kg/(m·s)).

While there is no theorem directly relating the non-dimensional Reynolds number to turbulence, flows at Reynolds numbers larger than 5000 are typically (but not necessarily) turbulent, while those at low Reynolds numbers usually remain laminar. In Poiseuille flow, for example, turbulence can first be sustained if the Reynolds number is larger than a critical value of about 2040;[18] moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000.


Heat and momentum transfer[edit]


Assume for a two-dimensional turbulent flow that one was able to locate a specific point in the fluid and measure the actual flow velocity v = (vx,vy) of every particle that passed through that point at any given time. Then one would find the actual flow velocity fluctuating about a mean value:

and similarly for temperature (T = T + T′) and pressure (P = P + P′), where the primed quantities denote fluctuations superposed to the mean. This decomposition of a flow variable into a mean value and a turbulent fluctuation was originally proposed by Osborne Reynolds in 1895, and is considered to be the beginning of the systematic mathematical analysis of turbulent flow, as a sub-field of fluid dynamics. While the mean values are taken as predictable variables determined by dynamics laws, the turbulent fluctuations are regarded as stochastic variables.



Kolmogorov's theory of 1941[edit]



Thus, Kolmogorov introduced a second hypothesis: for very high Reynolds numbers the statistics of small scales are universally and uniquely determined by the kinematic viscosity ν and the rate of energy dissipation ε. With only these two parameters, the unique length that can be formed by dimensional analysis is



Hence, a third hypothesis of Kolmogorov was that at very high Reynolds number the statistics of scales in the range ηrL are universally and uniquely determined by the scale r and the rate of energy dissipation ε.



where 1/2uiui is the mean turbulent kinetic energy of the flow. The wavenumber k corresponding to length scale r is k = /r. Therefore, by dimensional analysis, the only possible form for the energy spectrum function according with the third Kolmogorov's hypothesis is




should have the same statistical distribution as






See also[edit]

References and notes[edit]

  2. ^ Ting, F. C. K.; Kirby, J. T. (1996). "Dynamics of surf-zone turbulence in a spilling breaker". Coastal Engineering. 27 (3–4): 131–160. doi:10.1016/0378-3839(95)00037-2. 
  3. ^ a b Tennekes, H.; Lumley, J. L. (1972). A First Course in Turbulence. MIT Press. 
  4. ^ Eames, I.; Flor, J. B. (January 17, 2011). "New developments in understanding interfacial processes in turbulent flows". Philosophical Transactions of the Royal Society A. doi:10.1098/rsta.2010.0332. 
  6. ^ Narasimha, R.; Rudra Kumar, S.; Prabhu, A.; Kailas, S. V. (2007). "Turbulent flux events in a nearly neutral atmospheric boundary layer". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 365 (1852): 841–858. Bibcode:2007RSPTA.365..841N. doi:10.1098/rsta.2006.1949. 
  7. ^ Trevethan, M.; Chanson, H. (2010). "Turbulence and Turbulent Flux Events in a Small Estuary". Environmental Fluid Mechanics. 10 (3): 345–368. doi:10.1007/s10652-009-9134-7. 
  9. ^ weizmann.ac.il
  10. ^ Marshak, Alex (2005). 3D radiative transfer in cloudy atmospheres. Springer. p. 76. ISBN 978-3-540-23958-1. 
  13. ^ Benzi, R.; Frisch, U. "Turbulence". Scholarpedia. 
  14. ^ Falkovich, G. "Cascade and scaling". Scholarpedia. 
  15. ^ Stull, Roland B. (1994). An Introduction to Boundary Layer Meteorology (reprint of 1st ed.). Dordrecht [u.a.]: Kluwer. p. 20. ISBN 978-90-277-2769-5. 
  16. ^ Falkovich, G. (2011). Fluid Mechanics. Cambridge University Press. [ISBN missing]
  17. ^ Sommerfeld, Arnold (1908). "Ein Beitrag zur hydrodynamischen Erkläerung der turbulenten Flüssigkeitsbewegüngen" [A Contribution to Hydrodynamic Explanation of Turbulent Fluid Motions]. International Congress of Mathematicians. 3: 116–124. 
  18. ^ Avila, K.; Moxey, D.; de Lozar, A.; Avila, M.; Barkley, D.; B. Hof (July 2011). "The Onset of Turbulence in Pipe Flow". Science. 333 (6039): 192–196. Bibcode:2011Sci...333..192A. doi:10.1126/science.1203223. 
  19. ^ Frisch, U. (1995). Turbulence: The Legacy of A. N. Kolmogorov. Cambridge University Press. ISBN 9780521457132. 
  20. ^ Mathieu, J.; Scott, J. (2000). An Introduction to Turbulent Flow. Cambridge University Press. [ISBN missing]

Further reading[edit]

External links[edit]