On the Delay and Inviscid Nature of Turbulent Break-away Separation in the High-Re Limit

We complement the recently achieved status quo of a self-consistent asymptotic theory: incompressible-flow separation from the perfectly smooth surface of a bluff rigid obstacle that perturbs an otherwise uniform flow in an unbounded domain. Here the globally formed Reynolds number, Re, takes on arbitrarily large values, and we are concerned with a long-standing challenge in boundary layer theory. Specifically, the external flow is sought in the class of potential flows with free streamlines, and the level of turbulence intensity, concentrated in the BL undergoing separation, is measured in terms of distinguished limits. Their particular choices categorise the type of the viscous-inviscid interaction mechanism governing local separation and the strength of its downstream delay when compared with laminar-flow separation. In the case of extreme retardation, this implies the selection of a fully attached potential flow around a closed body, the singular member of the family of free-streamline flows. In turn, the asymptotic theory predicts the distance of the separation from the thus emerging rear stagnation point or trailing edge of the body to vanish at a rate much weaker than that given by 1/ lnRe, which plays a crucial role in the scaling of firmly attached turbulent BLs. Notably, the overall theory only resorts to specific turbulence closures when it comes to numerical studies. 1 Motivation and Attached-Flow Structure Gross separation of a nominally two-dimensional (most developed) turbulent boundary layer (BL) in subsonic flow around a bluff body in the limit of large values of the globally formed Reynolds number, Re, has regained awareness in the last years, Bernhard Scheichl Vienna University of Technology, Institute of Fluid Mechanics and Heat Transfer, Tower BA/E322, Getreidemarkt 9, 1060 Vienna, e-mail: [email protected] AC2T research GmbH (Austrian Center of Competence for Tribology), Viktor-Kaplan-Straße 2C, 2700 Wiener Neustadt, e-mail: [email protected]