Chaotic motion of an array of vortices above a flat wall.

The trajectories of three inviscid point vortices above a flat wall were investigated numerically. The behaviour of the trajectories was characterized by detailed power spectra, phase portraits, Poincare sections, and estimates of the Lyapunov exponent spectrum. For certain initial conditions, the trajectories are regular and confined to a two torus in phase space. However, chaotic behaviour that sets in as one of the vortices is initially placed closer to the unstable point of the system. In the chaotic regime, the system also exhibits large scale intermittency. Analytical expressions for the near and far field noise, generated by the motion of the vortices, were also obtained. It was found that in the presence of a flat boundary, this motion does not contribute to any dipole field noise radiation, but is characterized by a quadruple structure to leading order. The near field pressure was computed numerically and it was found that the chaotic behaviour of the vortex trajectories results in broadband noise.