Response to rotating forcing of the von-Kármán disk boundary layer

Abstract

In the present experimental investigation of the three-dimensional boundary layer due to a disk rotating in otherwise still air, the aim is to study the response to a radially localized perturbation applied with a prescribed relative frequency with respect to the disk. The response to localized rotating forcing is measured with a hot-wire probe. The rotation rate of the forcing element is controlled independently of the disk rotation rate, and the dynamics of the spatial response is studied as a function of the ratio between the two rotation rates. The theoretically expected disturbance trajectories are derived from an instability analysis based on the exact local dispersion relations computed from the complete linearized Navier-Stokes equations. Theoretical predictions and experimental measurements are shown to be in good agreement.