On the Abrupt Turbulent Reattachment Downstream of Leading-Edge Laminar Separation

A theoretical investigation of unsteady marginal separations, in a classical unsteady boundary layer, is described. This suggests that the nonlinear properties of such separations may be largely responsible, at least initially, for the central features often observed experimentally in the abrupt turbulent reattachment of eddies that follow laminar separation near the leading edges of aerofoils. The theory reduces the local flow problem to the solution of a nonlinear integro-partial differential equation for the unknown scaled skin friction, which is also proportional to the decrement in displacement locally. Numerical solutions followed by linear and nonlinear analysis show that all short-length small disturbances are unstable whenever reversed flow occurs; but for sufficiently confined initial conditions the instabilities accumulate in such a way that a breakdown is forced after a finite time. In the nonlinear breakdown a double structure arises near the point of collapse, with an effective 'shock' taking the flow abruptly from the reversed sense just upstream to the forward sense just downstream. This predicted shock forms the suggested possible link with the sudden transition and turbulent reattachment of laminar eddies in practice, at rounded leading edges. Discussions of the turbulence effects, of the related phenomenon of dynamic stall, of other instabilities present, and of the theoretical repercussions of the work are presented also.