Instability of three-dimensional boundary layers due to streamline curvature

Abstract

Investigated are the fundamental roles of the curvature of external streamlines in the stability of three-dimensional boundary layers, the partial differential equations governing small disturbances superimposed on the basic flows are modeled by a simple system of ordinary differential equations, which include a nondimensional parameter denoting magnitude of the streamline curvature. The eigenvalue problem posed by the model equations is numerically solved to evaluate effects of this parameter on critical Reynolds numbers of the Falkner-Skan-Cooke family of three-dimensional velocity profiles. Computational results predict the possibility of a new instability, essentially due to the streamline curvature, of the centrifugal type similar to the Tayior-Gortler instability caused by a concave curvature of the walL

STABILITY AND TRANSITION OF THREE-DIMENSIONAL BOUNDARY LAYERS

“…A somewhat different approach to the rotating-disk problem is taken in a series of papers by Itoh (1994Itoh ( , 1996Itoh ( , 1997Itoh ( , 1998, Buck & Takagi (1997), Takagi et al ( , 2000, and Buck et al (2000). Itoh (1994) formulated the linearstability problem to explicitly include the curvature of the inviscid streamline at the boundary-layer edge. He found that strongly curved inviscid streamlines produce a centrifugal-type instability similar to the Görtler instability on concave walls (Saric 1994).…”

Multi-Instability Analysis of Swept-Wing Boundary Layers Part 1. A Nonparallel Model of Stability Equations

“…It is also deduced that the cross-flow instability of three-dimensional boundary layers is not greatly affected by the nonparallelism of order R −1 , because this instability is of an inviscid inflection-point type. However the streamline-curvature instability, recently found to occur in three-dimensional boundary layers, [3][4][5] is of centrifugal type due to the curvature of external streamlines; therefore it cannot be described by the O-S equation, which ignores curvature effects of the nonparallel terms.…”

IUTAM Symposium on Laminar-Turbulent Transition

“…Theoretical analyses by Itoh (1994Itoh ( , 1996a show that the streamline curvature destabilizes the flow in the attachment-line region, while the wall curvature has an attenuating effect as has been already shown, and that a new instability is produced by the curvature of external streamlines and yields unsteady disturbances of longitudinal-vortex type like travel-ing waves induced by the cross-flow instability. It is also found that this new instability, labeled the streamline-curvature (referred to as S-C henceforth) instability, is really much weaker than cross-flow (C-F) instability in conventional geometric configurations.…”

“…This model was vertically set at a sweep angle of 50º in a test section 5.5m in width by 6.5m in height and 9m in length of the Lowspeed Wind Tunnel of the JAXA. More details are shown in Takagi and Itoh (1994). A tiny hole with a diameter of 0.6mm was drilled at the azimuthal angle =20º from the attachment line in order to introduce an artificial acoustic disturbance into laminar boundary layer by means of a loud speaker installed underneath the hole.…”