THE STABILITY OF ROTATING-DISC BOUNDARY-LAYER FLOW OVER A COMPLIANT WALL .2. ABSOLUTE INSTABILITY

A numerical study has been undertaken of the influence of a compliant boundary on absolute instability. In a certain parameter range absolut e instability occurs in the boundary layer on a rotating disc, thereby instigating rapid transition to turbulence. The conventional use of w all compliance as a laminar-flow control technique has been to lower g rowth rates of convective instabilities. This has the effect of reduci ng amplification of disturbances as they propagate downstream. For abs olute instability, however, only the suppression of its onset would be a significant gain. This paper addresses the question of whether pass ive wall compliance can be advantageous when absolute instability exis ts in a boundary layer. A theoretical model of a single-layer viscoela stic compliant wall was used in conjunction with the sixth-order syste m of differential equations which govern the stability of the boundary -layer flow over a rotating disc. The absolute/convective nature of th e flow was ascertained by using a spatio-temporal analysis. Pinch-poin t singularities of the dispersion relation and a point of zero group v elocity identify the presence of absolute instability. It was found th at only a low level of wall compliance was enough to delay the appeara nce of absolute instability to higher Reynolds numbers. Beyond a criti cal level of wall compliance results suggest that complete suppression of absolute instability is possible. This would then remove a major r oute to transition in the rotating-disc boundary layer.