Numerical studies of bypass transition in the Blasius boundary layer

Experimental findings show that transition from laminar to turbulent flow may occur also if the exponentially growing perturbations, eigensolutions to the linearised disturbance equations, are damped. An alternative non-modal growth mechanism has been recently identified, also based on the linear approximation. This consists of the transient growth of streamwise elongated disturbances, with regions of positive and negative streamwise velocity alternating in the spanwise direction, called streaks. These perturbation are seen to appear in boundary layers exposed to significant levels of free-stream turbulence. The effect of the streaks on the stability and transition of the Blasius boundary layer is investigated in this thesis. The analysis considers the steady spanwise-periodic streaks arising from the nonlinear evolution of the initial disturbances leading to the maximum transient energy growth. In the absence of streaks, the Blasius profile supports the viscous exponential growth of the Tollmien-Schlichting waves. It is found that increasing the streak amplitude these two-dimensional unstable waves evolve into three-dimensional spanwiseperiodic waves which are less unstable. The latter can be completely stabilised above a threshold amplitude. Further increasing the streak amplitude, the boundary layer is again unstable. The new instability is of different character, being driven by the inflectional profiles associated with the spanwise modulated flow. In particular, it is shown that, for the particular class of steady streaks considered, the most amplified modes are antisymmetric and lead to spanwise oscillations of the low-speed streak (sinuous scenario). The transition of the streak is then characterised by the appearance of quasi-streamwise vortices following the meandering of the streak. Simulations of a boundary layer subjected to high levels of free-stream turbulence have been performed. The receptivity of the boundary layer to the external perturbation is studied in detail. It is shown that two mechanisms are active, a linear and a nonlinear one, and their relative importance is discussed. The breakdown of the unsteady asymmetric streaks forming in the boundary layer under free-stream turbulence is shown to be characterised by structures similar to those observed both in the sinuous breakdown of steady streaks and in the varicose scenario, with the former being the most frequently observed. Descriptors: Fluid mechanics, laminar-turbulent transition, boundary layer flow, transient growth, streamwise streaks, lift-up effect, receptivity, free-stream turbulence, secondary instability, Direct Numerical Simulation.