On the interaction of a vortex with a local roughness on the rigid surface

Disturbances that a potential vortex excites in a boundary layer when moving over a hump or dent on an otherwise flat plate are considered analytically and numerically. Specific features of this problem are determined by the fact that the vortex is stuck with a fixed fluid particle, as a result a relationship between the excess pressure and components of the velocity field induced by the vortex becomes nonlinear even if its strength is small. Mathematical formulation of the problem in terms of canonical variables involves four similarity parameters for any shape of the roughness. An analogy between the process under consideration and the interaction of an acoustic pulse with a boundary layer over a small obstacle on the bottom is pointed out. Results of numerical solution of the problem posed allow to trace the wavepacket evolution depending on the vortex intensity.