Steady and unsteady 3D interactive boundary layers

The paper describes theoretical and computational research on 3D steady and unsteady flows at medium-to-high Reynolds numbers (Re), aimed at increasing understanding of 3D separation and boundary-layer transition. Concerning steady 3D flows first, an interactive-boundary-layer (IBL) formulation for 3D laminar flow of an incompressible fluid over a surface-mounted obstacle is addressed computationally and compared with other methods at various Re. The computational approach is designed deliberately to capture the extra ellipicity present due to the three-dimensionality, making use of skewed shears in linear quasi-planar sweeps of the boundary layer and local updating in the 3D interaction law. Results including separation are presented for a range of Re and obstacle heights, together with grid-effect studies, and comparisons are made, first with triple-deck predictions for high Re and, second, with an alternative IBL approach presented in a companion work. The latter and the current work together yield a broad agreement on predictions for the 3D flow, stretching from the triple-deck through the IBL to thin-layer Navier-Stokes predictions, over a wide range of Re. Second, the computational approach is extended to unsteady 3D flows, for the triple-deck limit including linear and nonlinear Tollmien-Schlichting waves. Results for small and nonsmall disturbances and comparisons are presented, showing fairly encouraging agreement between theory, computations and experiments.