Abstract:
Energy can flow through tubes filled with air governed by the laws of fluid dynamics, even in the violent form of shock waves. Energy also can flow through such systems as oscillations of small amplitude, which are governed by the equations of linear acoustics. What happens in the regime between? Calculations performed upon complaint of excessive low-frequency noise during alternate blasting for two long parallel railway tunnels indicated that particle velocities were a substantial fraction of the speed of sound at the tunnels' mouths---between the regimes of shock waves and linear resonances. A Strouhal calculation suggested that vortices were the likely source: A sequence of counter-rotating vortices was being propelled out of the tunnels' mouths, generating a powerful monopole source at 12 Hz. Modern noise consultants were baffled, but Lord Rayleigh had solved the system a century before, as a compound nonlinear eigenvalue problem, necessarily taking viscosity into account. The blasting engineers drove small cross-bores between the tunnels, sucking circulating fluid out of the vortices, reducing power, and quieting neighbors. The experiment should be repeated at a smaller scale with better instruments under controlled conditions.