Boundary Layer

Compared to laminar boundary layer, turbulent boundary layers produce stronger drag, grow faster and exhibit stronger resistance to separation.

Growth Rate of Boundary Layers

Hand-waving approach think in terms of the shear stress transmitting the influence of the no-slip boundary condition at the wall out into the free stream also one can think in terms of vorticity being created at the leading edge and then diffusing out into the free stream.

At each point in the flow we define two time scales, t_long and t _trans .

t_long longitudinal time scale, time required to convect free-stream fluid.

t_trans transverse time scale, time required to diffuse in the normal to the flow

Figure 2.1

Consider any point in the flow field and compare the time scales there:

There are three possibilities:

(i) t_long << t_trans

the flow at the point under consideration is dominated by the free stream and the point must lie outside the boundary layer.

(ii) t_long >> t_trans

the flow at the point under consideration is strongly influenced by the presence of the wall and the point must lie within the boundary layer.

(iii) Another possibility is t_long t_trans

which means

or

A familiar result, valid for Laminar bounadry layer.