Boundary layer stability on a rotating disk with corotation of the surrounding fluid
The paper treats the linear stability problem for the flow in the boundary layer on a rotating disk in a corotating fluid (generalized Karman problem). For values of \(\sigma\) (the ratio of angular velocity of the fluid and the disk) between \(\sigma =0\) (Karman flow) and \(\sigma=\infty\) (Bödewadt flow), the problem is solved by the collocation method. For all \(\sigma\geq 0\) the lower critical Reynolds number is determined by A-type instability waves typical of Eckman layers. B-type instabilities, associated with the occurrence of an inflection point in the velocity profile, typically manifest themselves as an ordered system of spiral vortices. Even though the critical Reynolds number of the A-type instability is several times smaller than the critical Reynolds number of spiral vortices, it has never been observed in rotating disk boundary layers. The authors argue that the low amplification rate of the A-type waves is the reason.
scientific article; zbMATH DE number 536775