Turbulence

If we place an obstacle, e.g., a sphere, at rest in the midst of a fluid stream, our physical intuition suggests Turbulence in the water below Niagara Falls. JLM Visuals. Reproduced by permission.


that the part of the fluid which is really in contact with the obstacle must be at rest. However, photographs taken in different laboratories appeared not to support this idea. In order to explain what was happening, Ludwig Prandtl (1875-1953) introduced the hypothesis of the "limiting layer," according to which in the immediate neighborhood of the obstacle there is a very thin layer of fluid whose velocity parallel to the surface of the object brows very rapidly, from zero at the surface itself to the velocity of the main body of fluid far from the object. This limiting layer is very thin upstream, but broadens downstream, i.e., behind the obstacle.

Inside the downstream limit layer the fluid begins to move backwards and in circles, until the eddies form when the Reynolds number is R = 5. As the fluid velocity grows, bringing R to a value of 70, the limit layer broadens still more downstream, forming what is called a "von Karman vortex street" after Theodor von Karman (born 1881). These eddies finally leave the vicinity of the obstacle and float away with the main fluid current. If R keeps increasing to values of 1000 or 2500, eddies become more frequent and the vortex street broadens still more, finally breaking up and forming a "turbulent wake." At this stage the motion of fluid particles is chaotic and varies in time.