# Fundamentals of turbulence

### From Thermal-FluidsPedia

Turbulent flow is the most commonly encountered type of viscous flow but its theoretical treatment is not as well developed as that for the laminar flow. Turbulent flow can be examined with particular attention paid to mechanism of the momentum and energy transfer.

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## Description of turbulence

In turbulent flow, the transport phenomena variables (i.e., *u, v, w, T, p*, etc.) always vary with time. For example, the magnitude and direction of the instantaneous velocity vector are different from those of the time-averaged velocity. While the instantaneous velocity in a turbulent flow is always time-dependent, the time averaged velocity can be either time-independent or time dependent. For any given location (x, y, z) and time t, the local instantaneous velocity can be expressed as a summation of its mean value and its fluctuation.

*See main article" Description of turbulence.*

## Time-averaged governing equations for turbulence

The transport phenomena equations including the Navier-Stokes and the energy equation are exact for solving the turbulent problem if their complete unsteady forms are solved. In general, this approach is not taken because of complexity and significant computer time requirement. In addition, the turbulent problems, in their gross aspect, are assumed steady state. Time averaging of transport phenomena equations should provide the net effect of the turbulent perturbation.

*See main article" Time-averaged governing equations for turbulence.*

## References

Faghri, A., Zhang, Y., and Howell, J. R., 2010, *Advanced Heat and Mass Transfer*, Global Digital Press, Columbia, MO.