“…Note the following three restrictions that lead to the specific form of the expansion (21), where consistency will be shown later: (i) eigensolutions that are due to matching with the flow quantities in the transitionalflow region have been omitted as they do not affect the main results of the subsequent analysis; (ii) it anticipates the relationship…”
Section: Iiia1 Viscous Wall Layermentioning
confidence: 99%
“…The idea behind the last assumption becomes clear immediately by inspection of the accordingly expanded BL equation 18, subject to the boundary conditions (12). Substituting the expansion (21) into Eqs. (18) and (12) then yields, after integration with respect to Y + by taking into account the scalings given by Eqs.…”
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.
“…Note the following three restrictions that lead to the specific form of the expansion (21), where consistency will be shown later: (i) eigensolutions that are due to matching with the flow quantities in the transitionalflow region have been omitted as they do not affect the main results of the subsequent analysis; (ii) it anticipates the relationship…”
Section: Iiia1 Viscous Wall Layermentioning
confidence: 99%
“…The idea behind the last assumption becomes clear immediately by inspection of the accordingly expanded BL equation 18, subject to the boundary conditions (12). Substituting the expansion (21) into Eqs. (18) and (12) then yields, after integration with respect to Y + by taking into account the scalings given by Eqs.…”
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.
“…The pressure gradient here also increases without limit in accordance with a power law (but a different one) with a coefficient which depends on the constant d . If d 1, the boundary layer in front of the corner point in the first approximation remains linear (Blasius), [9][10][11] exactly the same as in the free stream. If d = O(1), then, due to the action of the pressure gradient its own boundary layer is generated with an Ackerberg-type velocity profile.…”
We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove a priori error estimates for the Galerkin method, and show the results of some numerical computations.
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