Multiple instabilities of three-dimensional boundary layers along a concave wall

Abstract

The initial stage of laminar turbulent transition in boundary layers on a swept wing is governed by two types of instability, namely, the Tollmien-Schlichting instability based on the effect of viscosity and the cross-flow instability associated with the twisted velocity distribution of three-dimensional boundary layers. If the flow is along a locally concave surface, there is another possibility, that of Taylor–Görtler instability induced by centrifugal force. The strength of these instabilities mainly depends upon local Reynolds number, magnitude and direction of the cross-flow, and local curvature of the wall. Thus a model system of linear equations is proposed to describe the initial development of disturbances through the three instabilities, and its eigensolutions are used to evaluate stability limits of the Falkner Skan-Cooke flow to those disturbances. The three types of disturbances can be distinguished from each other by definite differences in the wavenumber and frequency regions. Three subregions in the parameter plane of cross-flow magnitude and wall curvature are determined in correspondence to the three instabilities, each of which gives the lowest value of critical Reynolds numbers in its own Subregion.