On the absolute instability of the attachment-line and swept-Hiemenz boundary layers

Recently it has been shown that flow over a rotating-disk is absolutely uns table. In this paper we investigate the absolute instability of the related swept-Hiemenz and attachment-line boundary-layer flows. The linearized sta bility equations are obtained and the eigenvalues of the dispersion relatio n are found by solving the full stability equations in Fourier-transform sp ace using a spectral method. Unlike previous work on this problem, no quasi -parallel approximation has been made and all the terms appearing in the st ability equations have been retained. We were unable to locate branch point s satisfying the Briggs-Bers criterion for the attachment-line boundary lay er suggesting that this flow is only convectively unstable. However, for th e swept-Hiemenz boundary layer our results show that this how becomes absol utely unstable (in the chordwise direction), starting from the leading-edge extending up to a chordwise position of approximately 310 for some particu lar spanwise Reynolds numbers. It is found that the retention of all the te rms in the full system of equations leads to results which are more unstabl e, in terms of absolute instability, than the Orr-Sommerfeld system studied by others. The techniques used here apply equally to other non-parallel tw o- and three-dimensional boundary-layer flows.