Laminar boundary-layer separation over a circular cylinder in uniform shear flow

By appealing to the classical boundary-layer theory, the present paper investigates the effect of the freestream shear on the separation of the laminar boundary layer around a circular cylinder. It is shown that on the side of the cylinder with faster freestream velocity the location of the separation point (point of vanishing wall shear) is virtually unaffected by the freestream shear, while on the other side of the cylinder a critical shear rate is observed. Below this critical value, separation occurs typically at the rear surface of the cylinder and is found to shift towards the downstream direction with increasing freestream shear. Above the critical shear rate, the boundary layer separates from the windward side of the cylinder. Further increase of the freestream shear then causes the separation point to move towards the upstream direction. The present findings may have important implication on the issue regarding to the orientation of the lift force exerting on the cylinder.