TY - JOUR
T1 - On the instability of flow in a streamwise corner
JF - Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences
SP - 201
LP - 210
M3 - 10.1098/rspa.1993.0057
VL - 441
IS - 1911
AU -
A2 -
Y1 - 1993/04/08
UR - http://rspa.royalsocietypublishing.org/content/441/1911/201.abstract
N2 - 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 Rer, associated with a spanwise location is significantly reduced as the corner is approached, being Rer = 54 approximately for spanwise distance of z* = 6x*R-1 from the corner compared with Rer = 322 approximately for z* = 20x*R-1, where x* measures downstream distance from the leading edges and R2 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.
ER -