A new analysis of the rotationally symmetric flow in the presence of an infinite rotating disk

Von Kármán swirling viscous flow produced by an infinite rotating disk is investigated, both analytically and numerically, when the fluid at infinity is in a state of rigid body rotation. The analytical solution branch of the problem considered are shown conveniently when the fluid at infinity is rotating with a different ratio, 0 ≤ s ≤ 1, of the angular velocity to that of the disk. As for − 0.1575 ≤ s < 0, the forward shooting technique by Runge-Kutta combined with Newton-Raphson method, different from previous conclusions, can still give effectively the first solution branch of dual solutions by Zandbergen and Dijkstra [11] who adopted a backward shooting technique. The solution branches of von Kármán swirling viscous flow are enriched. A possible explanation is made from both mathematical and physical perspectives.