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This paper is devoted to an experimental investigation of the distributed receptivity of a laminar swept-wing boundary layer to unsteady freestream vortices with streamwise orientation of the vorticity vector. The experiments were performed on a model of a swept wing with a sweep angle of at fully controlled disturbance conditions with freestream vortices generated by a special disturbance source. It is found that the unsteady streamwise vortices are able to provide very efficient excitation of cross-flow instability modes without requiring the presence of any surface non-uniformities. The developed experimental approach is shown to allow us to perform a detailed quantitative investigation of the mechanism of distributed excitation of unsteady boundary-layer disturbances due to scattering of freestream vortices on natural base-flow non-uniformity. This mechanism has been studied experimentally in detail. Part 1 of the present investigation (Borodulin et al., J. Fluid Mech., vol. 908, 2021, A14) was devoted to the description of the experimental approach and the base-flow structure, the method of excitation of fully controlled streamwise-elongated freestream vortices, the results of measurements of structure of these vortices and the experimental evidence of high efficiency of the distributed vortex receptivity mechanism under study. Meanwhile, the present paper (Part 2) is devoted to: (a) theoretical background and definition of the distributed receptivity coefficients and (b) obtaining experimental quantitative characteristics of the distributed vortex receptivity including values of the corresponding receptivity coefficients for their three different definitions as functions of the disturbance frequency, spanwise wavenumber and wave propagation angle.

This paper is devoted to an experimental investigation of receptivity of a laminar swept-wing boundary layer due to scattering of free-stream vortices on localized (in the streamwise direction) surface vibrations. The experiments were conducted under completely controlled disturbance conditions by means of a hot-wire anemometer on a model of a swept wing with a sweep angle of 25°. Both the free-stream vortices and the surface vibrations were generated by disturbance sources; their frequency–wavenumber spectra were measured thoroughly. The free-stream vorticity vectors were directed perpendicular to the incident-flow velocity vector and parallel to the swept-wing-model surface. The linearity of the receptivity mechanism under investigation (in a sense that the corresponding receptivity coefficients are independent of the disturbances amplitudes) has been checked carefully. The main goal of this experiment was to estimate the vibration-vortex receptivity coefficients as functions of the disturbance frequency, spanwise wavenumber and vortex offset parameter. This goal has been attained. Being defined in Fourier space, the obtained receptivity coefficients are independent of the specific surface vibration shape and can be used for verification of various receptivity theories.

The present experimental study is devoted to examination of the vortex receptivity mechanism associated with excitation of unsteady cross-flow (CF) waves due to scattering of unsteady free-stream vortices on localized steady surface non-uniformities (roughness). The measurements are carried out in a low-turbulence wind tunnel by means of a hot-wire anemometer in a boundary layer developing over a $25\textdegree $ swept-wing model. The harmonic-in-time free-stream vortices were excited by a thin vibrating wire located upstream of the experimental-model leading edge and represented a kind of small-amplitude von Kármán vortex street with spanwise orientation of the generated instantaneous vorticity vectors. The controlled roughness elements (the so-called ‘phased roughness’) were placed on the model surface. This roughness had a special shape, which provided excitation of CF-waves having basically some predetermined (required) spanwise wavenumbers. The linearity of the stability and receptivity mechanisms under study was checked accurately by means of variation of both the free-stream-vortex amplitude and the surface roughness height. These experiments were directed to obtaining the amplitudes and phases of the vortex-roughness receptivity coefficients for a number of vortex disturbance frequencies. The vortex street position with respect to the model surface (the vortex offset parameter) was also varied. The receptivity characteristics obtained experimentally in Fourier space are independent of the particular roughness shape, and can be used for validation of receptivity theories.

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.