- For a turbulent flow over a flat plate,
The turbulent boundary layer continues to grow in thickness, with a small region below it called a viscous sublayer. In this sub layer, the flow is well behaved,just as the laminar boundary layer (Fig. 32.3)
Fig. 32.3 Laminar - turbulent transition
Illustration
- Observe that at a certain axial location, the laminar boundary layer tends to become unstable. Physically this means that the disturbances in the flow grow in amplitude at this location.
Free stream turbulence, wall roughness and acoustic signals may be among the sources of such disturbances. Transition to turbulent flow is thus initiated with the instability in laminar flow
- The possibility of instability in boundary layer was felt by Prandtl as early as 1912.The theoretical analysis of Tollmien and Schlichting showed that unstable waves could exist if the Reynolds number was 575.
The Reynolds number was defined as
where  is the free stream velocity ,  is the displacement thickness and  is the kinematic viscosity .
- Taylor developed an alternate theory, which assumed that the transition is caused by a momentary separation at the boundary layer associated with the free stream turbulence. In a pipe flow the initiation of turbulence is usually observed at Reynolds numbers (
 )in the range of 2000 to 2700.
The development starts with a laminar profile, undergoes a transition, changes over to turbulent profile and then stays turbulent thereafter (Fig. 32.4). The length of development is of the order of 25 to 40 diameters of the pipe.
Fig. 32.4 Development of turbulent flow in a circular duct
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