The trajectories of three inviscid point vortices above a flat wall were investigated numerically. The behavior of the trajectories was characterized by detailed power spectra, phase portraits, Poincaré 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 behavior 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 quadrupole structure to leading order. The near-field pressure was computed numerically and it was found that the chaotic behavior of the vortex trajectories results in broadband noise.
ASJC Scopus subject areas