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

Abstract

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 boundary layer 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 $1/\ln Re$, which plays a crucial role in the scaling of firmly attached turbulent boundary layers. Notably, the overall theory only resorts to specific turbulence closures when it comes to numerical v investigations.