On Stability and Transition in Three-Dimensional Flows

The usefulness of the e" method for predicting transition in two-dimensional and axially symmetric flows is well established. In order to extend the method to three-dimensi onal parallel shear flows, it is first necessary to establish a relationship between a and /?, the complex wave numbers in two perpendicular directions in the plane of flow. We suggest that this may be done by making use of group velocity concepts which lead'to the requirement da/dp = - tan<£, where 0 is real and denotes the direction of propagation of centered disturbances. As a paradigm of this approach, the rotating disk is studied. It is established that the critical Reynolds number is 176, that the principal disturbances to the laminar flow travel outwards and at an angle — - 8 deg to the direction of motion of the disk, while the appropriate value of n is —20. The observed direction of propagation of disturbance is at - - 13 deg to the direction of motion of the disk. The generally accepted value of n is -9, much less than that found here.