THE LINEAR-STABILITY OF BOUNDARY-LAYER FLOW OVER COMPLIANT WALLS - EFFECTS OF BOUNDARY-LAYER GROWTH

The linear stability of boundary-layer flow over compliant or flexible surfaces has been studied by Carpenter and Garrad (1985), Yeo (1988) and others on the assumption of local flow parallelism. This assumptio n is valid at large Reynolds numbers. Nonparallel effects due to growt h of the boundary layer gain in significance and importance as one get s to lower Reynolds number. This is especially so for a compliant surf ace, which can sustain a variety of wall-related instabilities in addi tion to the Tollmien-Schlichting instabilities (TSI) that are found ov er rigid surfaces. The present paper investigates the influence of bou ndary-layer non-parallelism on the TSI and wall-related travelling-wav e flutter (TWF) on compliant layers. Corrections to the growth rate of locally parallel theory for boundary-layer non-parallelism are obtain ed through a multiple-scale analysis. The results indicate that flow n on-parallelism has an overall destabilizing influence on the TSI and T WF. Flow non-parallelism is also found to have a very strong destabili zing effect on the branch of TWF that stretches to low Reynolds number . The results obtained have important implications for the design and use of compliant layers at low Reynolds numbers.