The wave pattern produced by a point source on a rotating disk

Abstract

It is pointed out that the boundary layer on a rotating disk is important in stability theory because it provides a particularly simple way to study the important phenomenon of crossflow instability. This type of instability is responsible for early transition on sweptback wings. Mack and Kendall (1983) have studied the wave patterns formed by harmonic point sources in a Blasius boundary layer on the basis that the source uniformly excites all oblique normal modes of the source frequency. The calculation procedure for planar boundary layers was modified to fit the different geometry of the rotating disk and the lack of an axis of symmetry. Calculations were performed of the wave pattern produced by a zero-frequency point source located at the Reynolds number of the artificial roughness element in an experiment conducted by Wilkinson and Malik (1983). The results provided in the present investigation confirm that the experimental wave pattern is a superposition of the complete azimuthal wavenumber spectrum of zero-frequency normal modes with uniform initial amplitude and phase.