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
led 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-flow-dominated transition on swept wings.
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