1 Characteristics

(Panton3 26.1,2)

Reynolds experimentally studied laminar pipe flow (Poiseuille flow) using a dye streakline. He showed that above a Reynolds number $Re_D$ (based on the pipe diameter) of roughly 2,300, the flow becomes unsteady and irregular, turbulent. (By carefully removing disturbances, laminar flow can be maintained at Reynolds numbers that are several times larger.)

$$\hbox{\epsffile{figures/reyexp.ps}}$$

For Blasius’ flat plate, the transition to turbulent flow occurs at a Reynolds number $Re_x$ (based on $x$) of roughly about 320,000. (For comparison with pipe flow, the Reynolds number based on the boundary layer thickness may be more fair. Taking, rather arbitrarily, $\delta=5/\sqrt{Re_x}$, $Re_\delta$ would be 2,800.) Again laminar flow can be maintained at Reynold numbers several times larger, by very carefully minimizing flow disturbances.

Typical characteristics of turbulent flows are:

• unsteady, irregular 3D vorticity fluctuations;
• large diffusion;
• large Reynolds numbers;
• large dissipation.
• local;
• self-sustaining;