Evolution of a Boundary Layer from Laminar Stagnation-Point Flow Towards Turbulent Separation

We present the most relevant recent findings that allow for a rational timeaveraged description of laminar–turbulent transition of an incompressible nominally two-dimensional and steady boundary layer along the impermeable surface of a rigid blunt body. Rigorous application of matched asymptotic expansions for sufficiently high values of both the Reynolds number and a turbulence-level gauge parameter shows that the presence of a leading-edge stagnation point is associated with the generation of a turbulent shear layer that exhibits an asymptotically small streamwise velocity deficit. Remarkably, however, the turbulence intensity never reaches its theoretically possible maximum that conforms to fully developed turbulent flow. 1 Motivation and Problem Formulation Although desirable for engineering applications, a reliable prediction of the flow past a more-or-less bluff body for realistically high values of the globally formed Reynolds number, Re, is presently still unavailable, notwithstanding the undeniable ongoing progress of computational methods like Direct Numerical and Large-Eddy Simulation. That is, a self-consistent comprehensive description of the time-mean process of gross separation that is essentially derived from first principles in the limit Re → ∞ yet provides a challenging problem of theoretical hydrodynamics. As an interesting step forwards, here we focus on the asymptotic structure of the attached boundary layer (BL) evolving from the stagnation point, S, of the external flow. Let the natural coordinates x, y along and perpendicular to the (perfectly smooth) body surface with origin in S, the corresponding Reynolds-averaged velocity components u, v, and the Reynolds stresses be non-dimensional with respect to a typical half-diameter L of the obstacle, the speed U of the incident parallel free-stream Bernhard Scheichl · Alfred Kluwick Institute of Fluid Mechanics and Heat Transfer, Resselgasse 3/E322, A-1040 Vienna, Austria, e-mail: [email protected],[email protected]