Linear eigenvalue calculations and spatial direct numerical simulations
(DNS) of
disturbance growth in Falkner–Skan–Cooke (FSC) boundary layers
have been
performed. The growth rates of the small-amplitude disturbances obtained
from the
DNS calculations show differences compared to linear local theory, i.e.
non-parallel
effects are present. With higher amplitude initial disturbances in the
DNS calculations,
saturated cross-flow vortices are obtained. In these vortices strong shear
layers
appear. When a small random disturbance is added to a saturated cross-flow
vortex,
a low-frequency mode is found located at the bottom shear layer of the
cross-flow
vortex and a high-frequency secondary instability is found at the upper
shear layer of
the cross-flow vortex. The growth rates of the secondary instabilities
are found from
detailed analysis of simulations of single-frequency disturbances. The
low-frequency
disturbance is amplified throughout the domain, but with a lower growth
rate than
the high-frequency disturbance, which is amplified only once the cross-flow
vortices
have started to saturate. The high-frequency disturbance has a growth rate
that is
considerably higher than the growth rates for the primary instabilities,
and it is
conjectured that the onset of the high-frequency instability is well correlated
with the
start of transition.
The Second Mode in High-enthalpy Boundary Layers in Chemical Non-equilibrium
