Dynamics of bypass transition behind roughness element subjected to pulses of free-stream turbulence

This study explores the dynamics of bypass transition of a zero pressure gradient boundary layer transitioning under the combined influence of an isolated roughness element with pulses of free-stream turbulence (FST). We consider a hemispherical roughness element placed over a flat plate, while the pulses of FST are introduced at the inlet, which is in contrast to continuous FST largely explored in the literature. For a fixed turbulence intensity and length scale, a series of eddy-resolving simulations are carried out to examine the effect of varying the pulsing frequency of FST. The flow behind the roughness element remains stable in the absence of FST for the subcritical Reynolds number Rek = 400 considered in this study. We observe that with the pulses of FST, the transition is triggered due to the interaction of the FST-induced Klebanoff streaks with the roughness-induced streamwise vortices. With an increase in the frequency of FST pulses, the boundary layer has less time to relax to its unperturbed state resulting in an earlier onset of transition. The transition onset predicted is in favorable agreement with the correlations proposed in the literature. We analyze the growth of disturbance kinetic energy, the shape of secondary instabilities over the streaks, and their phase speeds in detail. The FST pulse convecting over the roughness element triggers the inner varicose modes in its near-wake region. The varicose modes decay rapidly further downstream and the well-known sinuous instabilities (or the outer modes) trigger transition via transient growth associated with convective instabilities. Such clear identification of the sinuous and varicose instabilities is not usually observed in cases with continuous FST, highlighting the importance of our study in applications involving transition under intermittent turbulence.