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
is the free stream velocity , 
)in the range of 2000 to 2700.
