In this paper we investigate the three-dimensional laminar incompressible steady flow
along a corner formed by joining two similar quarter-infinite unswept wedges along
a side-edge. We show that a four-region construction of the potential flow arises
naturally for this flow problem, the formulation being generally valid for a corner of
an arbitrary angle (π−2α), including the limiting cases of semi- and quarter-infinite
flat-plate configurations. This construction leads to five distinct three-dimensional
boundary-layer regions, whereby both the spanwise length and velocity scales of the
blending intermediate layers are O(δ), with Re−1/2 [Lt ] δ [Lt ] 1, Re being a reference
Reynolds number supposed to be large. This reveals crucial differences between
concave and convex corner flows. For the latter flow regime, the corner-layer motion
is shown to be mainly controlled by the secondary flow which effectively reduces to
that past sharp wedges with solutions being unique and existing only for favourable
streamwise pressure gradients. In this regime, the corner-layer thickness is shown
to be O(Re−0.5+α/π/δ2α/π), −½π [les ] α [les ] 0, which is much smaller than O(Re−1/2) for
concave corner flows.Crucially, our numerical results show conclusively that, for α ≠ 0, closed streamwise
symmetrically disposed vortices are generated inside the intermediate layers, confirming
thus the prediction made by Moore (1956) for a rectangular corner, which has so
far remained unconfirmed in the literature.For almost planar corners, three-dimensional corner boundary-layer features are
shown, as in (Smith 1975), to arise when α ∼ O(1/ln Re). On the other hand, we
show that the flow past a quarter-infinite flat plate would be attained when both
values of the streamwise pressure gradient and external corner angle (π+2α) become
O(1/ln Re) or smaller.Numerical results for all these flow regimes are presented and discussed.
Three-dimensional instabilities and negative eddy viscosity in thin-layer flows