Turbulence

Abstract

The Reynolds number of flow

$$ Re = \frac{{\nu *L*}}{{v*}} $$

(2.1)

gives a measure of the importance of inertial related to viscous forces. Experiments show that all flows become unstable above a certain Reynolds number. Below values of the so-called critical Reynolds number Re _crit the flow is smooth and adjacent layers of fluid slide past each other in an orderly regime. This regime is called laminar flow. At Reynolds numbers larger than the critical value a complicated series of physical events takes place which eventually result in a radical change of the flow behavior. Finally, the flow becomes turbulent, i. e. velocity and other flow properties become chaotic and random. The flow is then unsteady even with constant boundary conditions. Turbulence is a kind of a chaotic and random state of motion. Nevertheless, velocity and pressure vary continuously with time within substantial regions of flow. Velocity fluctuations associated with turbulence give rise to additional stresses on the fluid — so-called Reynolds stresses. Examples of turbulent flows are: free turbulent flows (jet flow), turbulent boundary layer flows.