Massive flow separation from the surface of a plane bluff obstacle in an incompressible uniform stream is addressed theoretically for large values of the global Reynolds numberRe. The analysis is motivated by a conclusion drawn from recent theoretical results which is corroborated by experimental findings but apparently contrasts with common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation never attains a fully developed turbulent state, even for arbitrarily largeRe. Consequently, the boundary layer exhibits a certain level of turbulence intensity that is linked with the separation process, governed by local viscous–inviscid interaction. Eventually, the latter mechanism is expected to be associated with rapid change of the separating shear layer towards a fully developed turbulent one. A self-consistent flow description in the vicinity of separation is derived, where the present study includes the predominantly turbulent region. We establish a criterion that acts to select the position of separation. The basic analysis here, which appears physically feasible and rational, is carried out without needing to resort to a specific turbulence closure.

We consider the asymptotic structure of a steady developed viscous thin film passing the sharp trailing edge of a horizontally aligned flat plate under the weak action of gravity acting vertically and surface tension. The surprisingly rich details of the flow in the immediate vicinity of the trailing edge are elucidated both analytically and numerically. As a central innovation, we demonstrate how streamline curvature serves to regularise the edge singularity apparent on larger scales via generic viscous–inviscid interaction. This is shown to be provoked by weak disturbances of accordingly strong exponential downstream growth, which we trace from the virtual origin of the flow towards the trailing edge. They represent a prototype of the precursor to free interaction in the most general sense, which, interestingly, has not attracted due attention previously. Moreover, we delineate how an increased effect of gravity involves marginally choked flow at the edge.

Symbols α Slenderness parameter β Control parameter, Eq. (13) χ Coupling parameter, Eq. (93) χ b Upper bound of χ, Eq. (95) δ BL thickness ℓ Mixing length, Eq. (8) ǫ Bifurcation parameter (redefined), Eq. (42) ε Notion for gauge function, Eqs. (18), (31) η,η Similarity variables based on s, Eq. (19), andŝ, Eq. (77) η,η,η Similarity variables, Eqs. (30), (35), (55) Γ Gamma function γ Bifurcation parameter, Eq. (15) κ V. Kármán constant, Eqs. (11), (135) λ, µ Invariance parameters, Eq. (120) ω Exponent, Eqs. (31), (36) φ Local scaling function, Eqs. (35), (37) ψ Stream function ρ, ϑ Polar coordinates, Eq. (71) ρ, ϑ Polar coordinates (UD), Eq. (110) σ TD length scale, Eq. (94) τ Surface friction, Eq. (135) θ Heaviside functioñ ν Kinematic viscosity ∆ BL thickness (BL solution), Eq. (6) Γ Upstream limit ofÛ s , Eqs. (94), (118), (124) Λ Strength of induced pressure, Eqs. (96), (101), (115) Ω Eigenvalue Ψ Stream function (BL solution), Eq. (6) Υ Shear stress gradient evaluated at surface, Eq. (126) Ξ, Φ Coefficients in asymptotic series, Eq. (127) ξ BL coordinate related to ∆, Eq. (12) ζ Auxiliary variable Superscripts * Onset of separation

The paper concerns a rational and physically feasible description of gross separation from the surface of a plane and more-or-less bluff obstacle in an incompressible and otherwise perfectly uniform stream for arbitrarily large values of the globally formed Reynolds number. The analysis is initialized by a remarkable conclusion drawn from recent theoretical results that is corroborated by experimental findings but apparently contrasts common reasoning: the attached boundary layer extending from the front stagnation point to the position of separation at the body surface never attains a fully developed turbulent state, even in the limit of infinite Reynolds number. As a consequence, the boundary layer exhibits a certain level of turbulence intensity that is determined by the separation process governed by locally strong viscous/inviscid flow interaction. This mechanism is expected to be associated with rapid transition of the separating shear layer towards an almost fully developed turbulent state. Here a rigorous asymptotic analysis, essentially carried out without resorting to a specific turbulent closure and supported by a numerical investigation, of the topology of the boundary layer flow close to separation is presented.