Sound emission during the scattering of Tollmien-Schlichting waves in a boundary layer on a nonuniform surface

Sound excitation during the propagation of a sinusoidal T-S wave in a boundary layer on a geometrically nonuniform rigid surface is analyzed in the framework of the piecewise-linear approximation of the velocity profile of the primary flow. Attention is given to nonuniformities which are small compared with the scales of viscous regions arising at the surface as a consequence of the attachment condition. The velocity field of the secondary flow produced as a result of surface nonuniformity is determined in the incompressible-fluid approximation. It is shown that the sound emission has a dipole character and is determined by shear stresses arising during wave scattering by the surface roughness and by volume inhomogeneities of the velocity field close to the surface. Numerical estimates of the emitted power are presented.