An asymptotic method for predicting stability characteristics, both stationary and travelling
crossflow vortices, over a variety of surface variations was created. These include
flat, convex and concave curved surfaces. Comparisons were made with two different
numerical methods (Parabolised Stability Equations and Velocity-Vorticity) and
good agreement, to within 5% of the numerical value of the crossflow mode streamwise
growth rate was met for both stationary and travelling modes initially for a flat
surface. An additional comparison was made with the streamwise growth rates to observe
the impact of including curvature and a small convex curvature surface variation
was used. Similar results were achieved for this study also. Likewise results for travelling
crossflow modes were with accordance with the numerical values.
To understand how effective this disturbance in penetrating the boundary-layer, receptivity
analysis was developed to analyse various mechanisms in the production of
crossflow vortices. A response function was established from the receptivity analysis
to calculate the efficiency of this process. The response function is largest near the
leading edge, meaning the disturbance is most effective at propagating into the boundary
layer there. This means that the approach qualitatively agrees with other research
methods. This is true for all surface curvatures and both crossflow modes. There
is an intriguing behaviour the response function exhibits for small concave curvature
with travelling modes at a moderate frequency. When we consider moderate spanwise
wavenumber, the response function is much larger than other modes or surface
variation and this could have repercussions for experiments. Careful consideration is
needed for this case and can be avoided with the aid of this research.
Finally, an asymptotic theory was created to analyse two-dimensional closed streamlines
for secondary instabilities. The first instability analysed was the elliptical instability,
due to the links to turbulence and the initial interest in this general problem.
The method anticipates the existence of short-wave three-dimensional disturbances on
a streamline at a distance away from the centre of the vortex of this secondary instability.
There was no limitation in the study for symmetrical known streamlines, the
analysis can be extended further to analyse any two-dimensional closed streamline
such as separation bubbles. With this in mind an observation was required to test this
hypothesis and the approach was tested on the structure inside a cavity, from which the
location and behaviour of the disturbance was correctly predicted.Open Acces
