A Generalized Method for the Stability of Incompressible Attachment-Line Flow

Abstract

The stability of small disturbances in the incompressible swept attachment-line boundary-layer flow is determined by solving the partial-differential eigenvalue problem. Previous theoretical investigations considered a special class of 2D disturbances resulting in ordinary differential equations. For the present method, the restrictive assumptions are relaxed to allow the treatment of more general disturbances. Results of the present analysis indicate that unstable disturbances other than the special 2D mode considered by earlier investigators do exist for $\bar{R} > 700$. Different modes with the same spanwise wavenumber are traveling with almost identical phase speeds, but the eigenfunctions show very distinct features. Yet, it is always the 2D mode which gives the highest growth rate and dictates the instability. As far as the 2D mode is concerned, present results are in excellent agreement with previous investigations, thus the generality of the current method is demonstrated. The advantage of the present approach is that it can be extended to compressible flows.

Research for both authors was supported by the National Aeronautics and Space Administration under NASA Contract No. NAS1-19299.