Instability Mechanisms and Intermittency Distribution in Adverse Pressure Gradient Attached and Separated Boundary Layers

Abstract: Direct numerical simulation has been carried out on one attached and two separated boundary layer flows (involving small and large separation) under the influence of an adverse pressure gradient. A unified picture of the pre-transitional boundary layer for the three cases has been provided that reveals a "mixed-mode" instability, involving contribution from instability waves and streamwise streaks. A time-frequency analysis of the transitional velocity signals has been performed which shows that as the Reynolds number decreases, the character of the time traces evolves continuously from a "spotty" behaviour (exhibiting distinct turbulent spots) for the attached case to a "non-spotty" behaviour (involving more "uniform" distribution of turbulent fluctuations in time) for the large separation case, encompassing the entire spectrum of transition scenarios. The variation of the intermittency factor within the transition zone is seen to compare well with the Narasimha universal intermittency distribution. We find that although the time variation of velocity for large separation is non-spotty (or more "uniform"), the spanwise variation of velocity is spotty, showing a clear clustering of high-wavenumber fluctuations separated by quasi-laminar regions. Thus, all the cases exhibit spottiness in the transition zone with different manifestations. We present a physical cartoon for the transition scenarios for the attached and separated cases, using the ideas of vortex-wall interaction and instability of spanwise vortical structures. We find that concentrated breakdown is exhibited by all the three cases near the transition onset and the spot breakdown processes are broadly consistent with the postulates underlying the universal intermittency distribution.