“How turbulent” is the boundary layer separating from a bluff body for arbitrarily large Reynolds numbers?

The paper deals with separation of a nominally steady and two-dimensional incompressible boundary layer from the smooth surface of a rigid blunt body in the presence of a front stagnation point, here denoted by PF . In agreement with earlier studies on the flow past a bluff body, it is argued that in the limit of vanishing viscosity, i.e. in the limit where the globally defined Reynolds number Re takes on arbitrarily large values, the solution of this problem is to be sought in the class of steady potential flows with free streamlines. Hence, it is first assumed that for sufficiently large values of Re the boundary layer upstream of separation is a fully developed turbulent one. Accordingly, it is demonstrated numerically and analytically, by adopting asymptotic techniques, how the well-known laminar flow taking place close to PF is gradually transformed into a fully developed turbulent boundary layer further downstream, which exhibits the well-established typical asymptotic two-layer splitting. However, as has been shown in a preceding study, this type of flow does not allow for a self-consistent rational description of separation, based on the nominally steady form of the equations of motion. From this result, supported by numerical and experimental evidence, the tentative but rather remarkable conclusion is drawn that the boundary layer along the smooth surface of a bluff body never attains a fully developed turbulent state, even in the limit Re → ∞. Most important, these findings are seen to be independent of the choice of a specific turbulence closure.