Numerical Investigation of Transitional Oscillatory Boundary Layers: Turbulence Quantities

This study investigates the organized flow structures and turbulence quantities in a transitional oscillatory boundary-layer flow over a smooth bed using a DNS model set up by the open-source framework Nektar++ (v5.2.0). The present model was validated against the results of a previous study involving a bypass transition mechanism in the intermittently turbulent regime. To trigger the initial perturbations, a roughness element was placed on the bed and removed at the very moment a two-dimensional vortex tube, caused by an inflectional-point shear-layer instability, was observed on it. Then, the turbulent spots where the flow experienced intense fluctuations in an otherwise laminar boundary layer were identified from the bed shear-stress distribution on the bed, which served as a reliable indicator of turbulence. These flow features emerged as the first sign of the initiation of turbulence. Several measurement points were selected to follow the bed shear-stress variations and to observe the spatial and temporal development of turbulent spots at a low-wave Reynolds number, (Formula presented.). Along with these observations, phase-resolved turbulence quantities were also investigated over successive half-cycles for the first time in the literature to understand how turbulence develops and spreads over the flow domain. The results show that the turbulence generated in the near-bed region becomes stronger in the deceleration stage due to the adverse pressure gradient and diffuses away from the bed during the subsequent phases of the developing oscillatory boundary-layer flow. The findings related to the turbulence quantities also indicate that the turbulence gradually evolves and spreads into the fluid domain in successive half-cycles.