Laminar-turbulent transition

The process of a laminar flow becoming turbulent is known as laminar-turbulent transition. This is an extraordinarily complicated process which at present is not fully understood. However, as the result of many decades of intensive research, certain features have become gradually clear, and it is known that the process proceeds through a series of stages. "Transitional flow" can refer to transition in either direction, that is laminar-turbulent transitional or turbulent-laminar transitional flow.

While the process applies to any fluid flow, it is most often used in the context of boundary layers due to their ubiquity in real fluid flows and their importance in many fluid-dynamic processes.

In 1883 Osborne Reynolds demonstrated the transition to turbulent flow in a classic experiment in which he examined the behaviour of water flow under different flow rates using a small jet of dyed water introduced into the centre of flow in a larger pipe.

The larger pipe was glass so the behaviour of the layer of dyed flow could be observed, and at the end of this pipe there was a flow control valve used to vary the water velocity inside the tube. When the velocity was low, the dyed layer remained distinct through the entire length of the large tube. When the velocity was increased, the layer broke up at a given point and diffused throughout the fluid's cross-section. The point at which this happened was the transition point from laminar to turbulent flow. Reynolds identified the governing parameter for the onset of this effect, which was a dimensionless constant later called the Reynolds number.

Reynolds found that the transition occurred between Re = 2000 and 13000, depending on the smoothness of the entry conditions. When extreme care is taken, the transition can even happen with Re as high as 40000. On the other hand, Re = 2000 appears to be about the lowest value obtained at a rough entrance.

Reynolds' publications in fluid dynamics began in the early 1870s. His final theoretical model published in the mid-1890s is still the standard mathematical framework used today. Examples of titles from his more groundbreaking reports are:

A boundary layer can transition to turbulence through a number of paths. Which path is realized physically depends on the initial conditions such as initial disturbance amplitude and surface roughness. The level of understanding of each phase varies greatly, from near complete understanding of primary mode growth to a near-complete lack of understanding of bypass mechanisms.

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