We present direct numerical simulations of the spatial development
of normal mode
perturbations to boundary layers with Falkner–Skan velocity profiles.
Values of the
pressure gradient parameter considered range from very small, i.e. nearly
conditions, to relatively large values corresponding to incipient separation.
all cases, we find that the most effective perturbation is one composed
of a plane
wave and a pair of oblique waves inclined at equal and opposite angles
to the primary
flow direction. The frequency of the oblique waves is half that of the
plane wave and because the conditions for resonance are satisfied exactly,
share a common critical layer, thus facilitating a strong interaction.
The oblique waves initially undergo a parametric type of subharmonic
but in accordance with recent analyses of non-equilibrium critical layers,
subsequently becomes fully coupled. From that point on, the amplification
modes, including the plane wave, substantially exceeds the predictions
stability theory. Good agreement is obtained with the experimental small
gradient results of Corke & Gruber (1996). Our growth rates are slightly
to slight differences in initial conditions (e.g. the angle of inclination
of the oblique
The spectral element method was used to discretize the Navier–Stokes
and the preconditioned conjugate gradient method was used to solve the
system of algebraic equations. At the inflow boundary, Orr–Sommerfeld
employed to provide the initial forcing, whereas the buffer domain technique
used at the outflow boundary to prevent convective wave reflection or upstream
propagation of spurious information.