Characterizing surface-gap effects on boundary-layer transition dominated by Tollmien–Schlichting instability

Abstract

Abstract Effects of gaps (rectangular surface cavities) on boundary-layer transition are investigated using a combination of linear stability theory and experiments, for boundary layers where the smooth-surface transition results from Tollmien–Schlichting (TS) instability. Results are presented for a wide range of gap characteristics, with the associated transition locations ranging from the smooth-surface location all the way forward to the gap location. The transition movement is well described by a variable $N$-factor, which links the gap characteristics to the level of instability amplification $e^N$ leading to transition. The gap effects on TS-wave transition are characterized by two limiting behaviours. For shallow gaps $d/w < 0.017$, the reduction in $N$-factor is a function of the gap depth $d$ and is independent of the gap width $w$. For deep gaps $d/w > 0.028$, the reduction in $N$-factor is a function of the gap width and is independent of the gap depth. When both the gap width and depth are sufficiently large relative to the displacement thickness $\delta ^*$, the TS-wave transition is bypassed, resulting in transition at the gap location. These behaviours are mapped out in terms of ($w/ \delta ^*$, $d/ \delta ^*$), providing a predictive model for gap effects on transition.