Stationary travelling cross-flow mode interactions on a rotating disk

This work involves the study of the development of Type 1 stationary and travelling cross-flow modes in the three-dimensional boundary layer over a rotating disk. In order to control the characteristics of the stationary modes, we utilized organized patterns of roughness which were applied to the disk surface. These consisted of ink dots which were equally spaced in the azimuthal direction at a fixed radius in order to enhance particular azimuthal wavenumbers. Logarithmic spiral patterns of dots were also used to enhance azimuthal wave angles. Velocity fluctuation time series were decomposed into the components corresponding to the stationary and travelling modes using the instantaneous disk position as a reference. Their development was documented through the linear and nonlinear stages leading to turbulence. The linear stage agreed well with linear stability predictions for both modes. In the nonlinear stage we documented a triad coupling between pairs of travelling modes and a stationary mode. The strongest of these was a difference interaction which lead to the growth of a low-azimuthal-number, stationary mode. This mode had the largest amplitude and appeared to dominate transition. In retrospect, we can observe the signs of this mechanism in past flow visualization (Kobayashi, Kohama & Takamadate 1980), and it can account for the 'jagged' front normally associated with cross-how-dominated transition on swept wings.