In 1883, Osborne Reynolds published his landmark paper on the transition from smooth, laminar flow to turbulent flow in cylindrical pipes. Drawing water through a horizontal glass pipe, Reynolds injected a narrow stream of dye and looked for the onset of eddies as he varied the flow velocity and the water viscosity (dependent on water temperature). He found that the transition to turbulence was very sensitive to disturbances and typically occurred above a critical value of about 2000 for the ratio of UD/ν, where U is the average (or bulk) velocity, D is the pipe diameter, and ν is the kinematic viscosity. This ratio, which parameterizes the relative strengths of inertial and viscous forces, is now known as the Reynolds number Re.
Understanding the nature of the transition to turbulence has been an ongoing quest ever since Reynolds’s first experiments (and was the subject of Werner Heisenberg’s PhD...
