INTERACTION OF A POTENTIAL VORTEX WITH A LOCAL ROUGHNESS ON A SMOOTH SURFACE

Disturbances generated by a potential vortex moving past a small hump or dent on the otherwise smooth flat plate are considered. Features pe culiar to this problem derive from the fact that the vortex is stuck w ith a fixed fluid particle; hence the nonlinear dependence of the pres sure on the induced velocity field ensues even if the vortex intensity tends to zero. Formulation of the problem on a flow in the viscous wa ll sublayer given in canonical variables involves four similarity para meters for any particular shape of a roughness. The parallels between the process at hand and sound scattering from a boundary layer with a small obstacle at the bottom are indicated. Results from numerical int egration of the boundary-value problem posed allow us to trace the evo lution of the wave-packet structure depending on the potential vortex intensity. Overlapping of the peak wings and formation of an almost co ntinuous spectrum in the Fourier decomposition of the signal serve as a guide for explaining the explosive development of the wave packet as distinct from the Tollmien-Schlichting wavetrain that has been regist ered experimentally. The theory developed is applied to discussing the so-called bypass mode of transition provoked by external turbulence. Special emphasis is laid on flows in gas turbine engines where bypass transition plays a dominant role owing to extremely high free-stream t urbulence levels.