The linear receptivity of a swept-wing three-dimensional boundary layer is studied
experimentally and theoretically. Cross-flow instability normal modes are excited by
means of surface vibration or roughness perturbations. The resulting disturbances are
investigated, and the normal modes are linked to the source perturbations. Experiments
are performed under controlled disturbance conditions with a time-harmonic
source that is localized in the spanwise direction. A localized surface vibration is
used to excite wave trains consisting of cross-flow instability waves. Normal oblique
modes (harmonic in time and space) are obtained by Fourier decomposition of
the wave trains. This provides the spatial variation of the normal modes and, in
particular, the initial amplitudes and phases of the modes at the source location.
The shape of the surface vibrator is measured and used to determine the complex
receptivity coefficients for the normal modes (i.e. for various spanwise wavenumbers,
wave propagation angles, and disturbance frequencies – including zero frequency).
The experimental receptivity coefficients are independent of the specific shape of
the surface non-uniformities and can be directly compared with calculations. The
theoretical work is based on a linear approximation to the disturbance source – valid
for small forcing amplitudes. Like earlier studies on roughness-induced receptivity, the
basic flow is locally assumed to satisfy the parallel-flow approximation. The modal
response for the cross-flow instability is determined from the residue associated with
the least-stable eigenmode.
A detailed quantitative comparison between the experimental and theoretical
receptivity characteristics is carried out. Good agreement is found for the
roughness–vibrational receptivity coefficients of the swept-wing boundary layer (especially for the
most-unstable cross-flow modes) over a range of disturbance frequencies and spanwise
wavenumbers. The theory correctly predicts the initial spectra for the travelling
and stationary cross-flow instabilities excited by the surface vibrations and surface
roughness, respectively. The good agreement between theory and experiment suggests
that the linear receptivity theory can be used effectively in engineering methods for
transition prediction. The experimental data can also be used for validation of other
theoretical approaches to the problem.