57 / 2019-09-15 11:00:25

The laminar-turbulent transition of oscillatory boundary layer

Boundary layer instability,Bypass transition

This work concerns the transition from laminar to turbulent in an oscillatory boundary layer. The oscillatory boundary layer, which is also known as Stokes boundary layer, can be generated by forcing a layer of fluid exhibiting a sinusoidal oscillation parallel to an infinitely long, smooth and flat plate or conversely by forcing the plate to oscillate sinusoidally in the horizontal direction. The transition from laminar to turbulent flow of the oscillatory boundary layer is a critical issue due to its close relevance to wave-induced physical processes such as sediment transport and biological blood flow in an artery and rich physics associated with the transition process. In this study, an isolated roughness element is set on an otherwise smoothed wall to trigger the initial disturbance. The two-dimensional coherent structure named as vortex tube evolves from the initial disturbance through inflection point instability. The present study reveals a complete scenario of the evolution of the vortex tubes and proposes a semi-analytical model to predict their motion based on the Helmholtz point-vortex equation. It is found that a 3-D or quasi-3D free-stream disturbance that evolves from the vortex tube can produce singularities inside the critical layer of Stokes boundary, which plays a critical role in triggering the non-modal and explosive transient growth of the perturbation, thus producing streaks, hairpin-like vortices and turbulence spots.