Abstract
The linear stability of an incompressible laminar flow in the blending boundary layer between the boundary layer in a 90° streamwise corner and a Blasius boundary layer well away from the corner is examined using a locally parallel flow approximation. It is shown that the magnitude of the cross flow in the boundary layer is too small to be a significant factor in the observed early transition in the blending layer. However, the influence of the outer boundary conditions associated with oblique modes of disturbances which are anti-symmetric about the bisector plane are shown to have a profound effect on the stability of the flow. As a result, the square root of the critical streamwise Reynolds number
R
er
, associated with a spanwise location is significantly reduced as the corner is approached, being R
er
= 54 approximately for spanwise distance of
z
* = 6
x
*
R
-1
from the corner compared with
R
er
= 322 approximately for
z
* = 20
x
*
R
-1
, where
x
* measures downstream distance from the leading edges and
R
2
is the streamwise Reynolds number. At
R
= 600, the growth rate of the most amplified mode of disturbance at the former location is over six times greater than that at the latter; the corresponding wave angle at the two locations is respectively 44° and 5°, approximately.
Cited by
15 articles.
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