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.

Collision of water wave solitons

“…5 and 6) initially, when the solitons are still separated, there are two maxima with a minimum Figure 15. Intersections of the curve (13) and (14) at identical pa- in between. During the collision the two solitons merge and only one maximum remains, the remnant of the other shows up only as a shoulder.…”

“…Hence approaching this limit can be interesting. This situation corresponds to case I. Maxima correspond to intersections of the line (14) with the two outer segments of the graph of (13). Obviously, as time goes on, the initially well separated solitons, while propagating in the same direction, get closer to each other, i.e., the distance between the two maxima decreases, then, without coalescing, their distance grows again.…”

“…(13) and (14). As time goes on, the coefficient of the power function (14) changes from zero to infinity, and the corresponding curve 4 "sweeps through" the curve (13). According to the possible shapes of curve (13) we observe different scenarios, according to the number of maxima.…”

“…Interest in environmental flows [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] both utilize and motivate theoretical work in nonlinear wave phenomena. Among these are solitons [19][20][21][22][23][24][25][26], which appear in many different situations and have applications in several other branches of physics [27,28].…”

Dispersion, dissipation and refraction of shock waves in acoustically treated turbofan inlets

“…(2) that whereas the resistive (dissipative) part of the wall impedance is independent of ω, the reactive part is not. The effects of dispersion on one-dimensional acoustic waves have been studied extensively by Sugimoto and his colleagues [34][35][36][37] using analysis, simulation and experiments. Specifically, the pressure traces shown in Figs.…”