Numerical studies of non-linear intrinsic streaks in the flat plate boundary layer

Abstract

The development of streaky perturbations near the leading edge of a flat plate boundary layer was analyzed by Luchini (1996) using a description of the flow linearized around the Blaius solution. He found that there is just one single streaky mode (periodic in the spanwise direction) that grows downstream from the leading edge. The presence of this mode in the linear approximation indicates that, for the complete non-linear problem, there is an one parameter family of streak solutions that grow from the leading edge of the boundary layer. This family of steady 3D non-linear intrinsic streaks (intrinsic because they appear in the complete absence of any free stream perturbation) was recently non-linearly computed, using the Reduced Navier-Stokes formulation to describe its downstream evolution far away from the linear region. In this work, we enlarge the analysis of the transversal structure of the streaks. Furthermore, the stability characteristics of the streaky boundary layer flow is presented using the three-dimensional Parabolized Stability Equations (PSE-3D) and spatial BiGlobal analysis formulations, which have been successfully employed in flows that are inhomogeneous in two directions and weakly dependent along the third spatial direction. The stability analysis results show that the intrinsic streaks damp Tollmien-Schlichting waves. This effect is increased as the amplitude of the streak grows. At a certain limit, as observed in linear optimal streaks, shear-layer modes become unstable, potentially producing bypass transition.