### ASA 126th Meeting Denver 1993 October 4-8

## 2aPAb13. The study of the influence of boundary layer effect upon the
standing wave in an open resonator.

**Yulia J. Benson
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*Math. & Mech. Dept., St. Petersburg, State Univ., 2 Bibliotechnaya pl.,
St. Petersburg 198904, Russia
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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.