Verification of acoustic solitary waves

Abstract

Experiments and numerical simulations are carried out to verify the existence of the acoustic solitary wave in an air-filled tube with an array of Helmholtz resonators connected. Following up previous work (Sugimoto et al. 1999), the experiments are improved by using a newly designed piston driver to launch an initially plane pressure pulse and also by extending the tube length from 7.4 m to 10.6 m. To highlight the effect of the array of resonators, the case with no array is also examined in parallel. Direct and indirect checks are made to verify the existence of the solitary wave. The former compares the profiles and propagation speeds of pulses measured experimentally to the solitary-wave solution. The latter checks the validity of nonlinear wave equations in describing real wave evolution in the tube. Solving an initial-value problem numerically with weakly lossy effects of boundary layers and jet loss at the throat of the resonator, comparison is made between measured and simulated evolution. The validity of the equations in the lossy case is necessary to maintain the existence of the solitary wave in the lossless limit. It is revealed that nonlinear wave equations originally derived for unidirectional propagation in the tube can provide a good description of the real evolution, with some allowance for phase shifts on reflection at both ends of the tube. In particular, it turns out that the lossy effects are described quantitatively well. By establishing the validity of the equations, it is concluded that the acoustic solitary wave exists.