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Transient growth in compressible boundary layer flow.
Abstract
The potential for transient growth in compressible boundary layers is
studied. Transient amplification is mathematically associated with a
non-orthogonal eigenvector basis, and can amplify disturbances although
the spectrum of the linearized evolution operator is entirely confined
to the stable half-plane. Compressible boundary layer flow shows a
large amount of transient growth over a wide range of parameter values.
The disturbance size is here measured by a positive definite energy
like quantity that has been derived such that pressure-related transfer
terms in its evolution equation mutually cancel. The maximum of the
transient growth is found for structures which are independent of the
streamwise direction and is found to scale with R/sup 2/. This suggests
that the transient growth originates from the same lift-up mechanism
found to give large growth in incompressible shear flows. The maximum
growth is also found to increase with Mach number. In compressible
flow, disturbances that experience optimal transient growth can be
excited naturally by a non-linear interaction of oblique unstable first
mode waves. Thus, a triggering of transient growth may account for the
difference in timescales between the fast oblique breakdown process and
traditional secondary instability.
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