J. Casacuberta, S. Westerbeek, J.A. Franco, K.J. Groot, S. Hickel, S. Hein, M. Kotsonis (2025)
Physical Review Fluids 10: 023902. doi: 10.1103/PhysRevFluids.10.023902
Direct numerical simulations have been performed to scrutinize the stationary velocity-perturbation streaks that form close downstream of two-dimensional forward-facing step of fixed height embedded in laminar incompressible swept-wing boundary-layer flow.
Stationary streaky structures are found to be universal to swept forward-facing-step flow subjected to three-dimensional perturbations in the incoming boundary layer. The streaks appear as alternating regions of streamise-velocity excess and deficit distributed along the step-edge direction and they develop spatially very close to the wall. A linear nonmodal growth mechanism attributed to the lift-up effect is shown to be mainly responsible for the local inception of the streaks at the upper step corner. It has been isolated that the cross-stream pattern of the fundamental (i.e., primary-wavelength) stationary crossflow perturbation in the incoming boundary layer lifts-up and pushes down low- and high-momentum fluid in adjacent regions of the highly sheared step flow. Under this principle, the lift-up effect gives rise to rapidly amplified and highly energetic streamwise streaks that inherently adopt the spanwise wavelength of the incoming boundary-layer perturbation. This has been argued by decomposing the perturbation field into components tangential (i.e., streamwise-aligned) and orthogonal (i.e., cross-stream-aligned) to the local orientation of base-flow streamlines and examining the mechanism of perturbation production, that is, the production term of the Reynolds-Orr equation. The analysis has revealed that a mechanism of base-flow deceleration, essentially a self-induction effect of streamwise perturbations, additionally contributes to feeding growth to the streaks in a region further downstream of the step.
The results of this work suggest that a wide range of incoming three-dimensional stationary perturbations have the potential to trigger structurally similar stationary near-wall streaks at the step. A key ingredient is the ability of the incoming three-dimensional cross-stream perturbation pattern to effectively redistribute base-flow momentum on interaction with the step flow. The lift-up effect is primarily responsible for the inception of streaks at the step. In turn, the streaks are a linear perturbation that develops as a sensitive reaction of the flow to three-dimensional perturbations in the incoming boundary layer. The present work establishes that the streaks are not a manifestation of additional crossflow instability of the distorted step-flow profiles.
Finally, linear stability analysis performed through the harmonic Navier-Stokes (HNS) method has confirmed that the streaks are a linear perturbation of forward-facing-step flow. The efficiency of the HNS class of computations allows for parametric studies of critical instability specifications. In this work, effects of spanwise wavelength have been assessed. Within the limits of the present parametric study, perturbation streaks universally form at the step independently of the wavelength of incoming boundary-layer perturbations, albeit the streaks exhibit different spatial amplification factors. An analysis of spanwise-velocity effects, i.e., representative of sweep-angle conditions, has similarly illustrated that stationary streaks form at the step independently of the local organization of the flow. The present work supports the universality of stationary perturbation streaks in three-dimensional laminar forward-facing-step flow, whose main structural features and initial amplitude are set by pertinent stationary three-dimensional perturbations in the incoming boundary layer.