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Distortion of the stagnation-point flow due to cross-stream vorticity in the external flow

The structure of the stagnation-point flow in the presence of weak steady cross-stream vorticity in the external flow is investigated. A specific case of the two-dimensional basic forward stagnation-point flow past a circular cylinder is considered with the external three-dimensional vortical disturbance taken to be periodic in the spanwise direction with a wavelength λ*≤λ*N=πD/(ReD)1/2, where D is the diameter of the cylinder and ReD is the flow Reynolds number. It is shown that the presence of weak but finite streamwise vorticity, with λ*≤λ*N in the external flow, can be supported by the flow in the stagnation zone, leading to a substructure of counterrotating streamwise eddies in the boundary layer. The magnitude of the streamwise vorticity in the boundary layer is found to match with that in the external flow for A* ^ X*N; it is of much smaller order for λ* > λ*N, which corresponds to a disturbance of the type considered by Hammerlin (1955).