On the Euler Stage of Turbulent Separation near the Trailing Edge of a Bluff Body

A novel self-consistent description of time-mean two-dimensional turbulent-boundary-layer flow separating from a bluff body at arbitrarily large globally formed Reynolds numbers is presented. Contrasting with previous approaches, the theory deals with a sufficient delay of flow detachment or, correspondingly, increase of the turbulence intensity so as to both settle the question of the actual position of separation and trigger a turbulent boundary layer exhibiting a large relative streamwise velocity deficit. At separation, a generic variation of the velocity profile close to the body surface with the third power of the distance from it is detected. The Euler stage resulting from the breakdown of the incident boundary layer and governed by its vorticity is envisaged in detail. Specifically, an analytical solution to the central linear vortex-flow problem could be established. This represents the essential ingredient for the understanding of the multi-layered substructure of the flow more close to the surface, which completes the picture of gross separation at the Euler scale. Most important, the analysis does not resort to any specific turbulence closure. Concerning the canonical situation of circular-cylinder flow, a first comparison between the predicted and publicly available experimentally obtained values of the separation angle is encouraging.