The stability of rotating-disc boundary-layer flow over a compliant wall. Part 2. Absolute instability

Abstract

A numerical study has been undertaken of the influence of a compliant boundary on absolute instability. In a certain parameter range absolute instability occurs in the boundary layer on a rotating disc, thereby instigating rapid transition to turbulence. The conventional use of wall compliance as a laminar-flow control technique has been to lower growth rates of convective instabilities. This has the effect of reducing amplification of disturbances as they propagate downstream. For absolute instability, however, only the suppression of its onset would be a significant gain. This paper addresses the question of whether passive wall compliance can be advantageous when absolute instability exists in a boundary layer.A theoretical model of a single-layer viscoelastic compliant wall was used in conjunction with the sixth-order system of differential equations which govern the stability of the boundary-layer flow over a rotating disc. The absolute/convective nature of the flow was ascertained by using a spatio-temporal analysis. Pinch-point singularities of the dispersion relation and a point of zero group velocity identify the presence of absolute instability. It was found that only a low level of wall compliance was enough to delay the appearance of absolute instability to higher Reynolds numbers. Beyond a critical level of wall compliance results suggest that complete suppression of absolute instability is possible. This would then remove a major route to transition in the rotating-disc boundary layer.