EXISTENCE OF FREE EDDIES IN A STREAMING STOKES FLOW

The uniform streaming Stokes flow past two equal separated cylinders is considered where the direction of flow is perpendicular to the line joining the centres. Because of Stokes's paradox, the problem reduces to solving for the first term of the inner expansion for low Reynolds number flow past two cylinders. It is found that fluid always moves through the gap separating the two cylinders no matter how small it is. When the gap width is less than 0.0446 times the cylinder radius, two free eddies form along the center line, one on either side of the gap. These eddies are completely isolated from the cylinder boundaries by the surrounding fluid and their appearance is a Stokes flow phenomenon not observed before. For smaller gaps-both free eddies and boundary eddies are present. These interlace as the cylinders approach forcing the fluid which moves through the gap to take a winding path. © 1979 Oxford University Press.