The dynamics and acoustics of viscous two-dimensional leapfrogging vortices

The dynamics and acoustics of two identical pairs of counter-rotating vortices in viscous compressible flow are investigated. Each finite-sized vortex has an initially Gaussian distribution of vorticity. The dilating vortex particle method—developed in previous work—is used for the high-fidelity solution of the full compressible Navier–Stokes equations in the nearfield and a portion of the acoustic field; the radiated sound is extrapolated from a Kirchhoff surface adjusted for mean flow. The trailing vortex pair periodically slips through the leading pair, producing a sharp acoustic pulse. During the ensuing relaxation period as the cores return to horizontal alignment, filaments of vorticity are stripped from the outer part of each vortex while its inner core remains intact, and a small oscillatory acoustic signal is emitted. In contrast to previous studies of inviscid patches of uniform vorticity, this signal is much weaker than the slip-through pulses. Passive particles in the vortex cores are used to explore the filament evolution and core dynamics. The elastic deformation of the inner core, which is a crucial source of sound in previous patch studies, is found to be insignificant to sound production in these smooth cores. Instead, the weak oscillatory component of sound is generated by the anchors of filamentary structures as they rotate about the core. After several slip-through cycles, the pairs coalesce to form a single counter-rotating pair, and the sound emissions become weak and sinusoidal.