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Article information
Secondary instability of cross-flow vortices in Falkner-Skan-Coke boundary layers.
| Authors: |
Högberg, M.,
Henningson, D.S.H.,
|
| Type: |
Article |
| Pubstate: |
Published |
| Journal: |
J. Fluid Mech. |
| Volume: |
368
339-357 |
| Year: |
1998 |
Abstract
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.
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