Yulia J. Benson
Math. & Mech. Dept., St. Petersburg, State Univ., 2 Bibliotechnaya pl., St. Petersburg 198904, Russia
A simplest model approach to the problem of the study of nonlinear processes in an open resonator is proposed here. It is based on the consideration of the only act of propagation---reflection of the wave in an open-ended tube. In other words, one can study the incoming wave distortion during wave propagation forward to the closed end (piston) and backward. According to the experimental data the process of oscillation in some cases is mostly defined by these distortions. For example, the experiment [B. Sturtevant, J. Fluid Mech. 63, pt. 1, 97--120 (1974)] predicts that a shock wave should be formed during the propagation considered. The numerical analysis of the standard Burgers' equation plus the term that was derived by Blackstock [D. T. Blackstock, J. Acoust. Soc. Am. 77, 2050--2053 (1985)] in order to describe an influence of the boundary layer at the walls on plane traveling waves allows one to conclude that an account of this effect permits one to obtain a good agreement with the results predicted by Sturtevant's experiment. Moreover such a statement can be regarded as an inverse problem, so that it is possible to restore the boundary condition using the experimental data.