Frequency selection mechanisms in the flow of a laminar boundary layer over a shallow cavity

Abstract

We investigate the flow over shallow cavities as a representa tive configuration for modelling small surface irregularities in wall-bounded shear flows. Due to t he globally stable nature of the flow, we perform a frequency response analysis, which shows a signifi cant potential for the amplification of disturbance kinetic energy by harmonic forcing within a cer tain frequency band. Shorter and more shallow cavities exhibit less amplified responses, while en ergy from the base flow can be extracted predominantly from forcing that impacts the cavity head-on . A structural sensitivity analysis, combined with a componentwise decomposition of the sensiti vity tensor, reveals the regions of the flow that act most effectively as amplifiers. We find that the fl ow inside the cavity plays a negligible role, whereas boundary layer modifications imme diately upstream and downstream of the cavity edges contribute significantly to the frequency r esponse. The same regions constitute preferred locations for implementing active or passive con trol strategies to manipulate the frequency response of the flow.