## Turbulence | onset of turbulence |

- examples of turbulence
- features
- onset of turbulence
- heat and momentum transfer
- kolmogorov's theory of 1941
- see also
- references and notes
- further reading
- external links

The onset of turbulence can be, to some extent, predicted by the ^{[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

With respect to

- laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion;
- turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic
eddies ,vortices and other flow instabilities.

The Reynolds number is defined as^{[17]}

where:

ρ is thedensity of the fluid (SI units : kg/m^{3})- v is a characteristic velocity of the fluid with respect to the object (m/s)
- L is a characteristic linear dimension (m)
μ is thedynamic viscosity of thefluid (Pa·s or N·s/m^{2}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 ^{[18]} moreover, the turbulence is generally interspersed with laminar flow until a larger Reynolds number of about 4000.

The transition occurs if the size of the object is gradually increased, or the