### ASA 124th Meeting New Orleans 1992 October

## 3aPA4. Nonlinear interaction of two simple waves in an open resonator.

**Yulia J. Benson
**

**
Sergey N. Makarov
**

**
**
*Math. and Mech. Dept., State St. Petersburg Univ., 2 Bibliotechnaya Pl.,
St. Petersburg 198904, Russia
*

*
*
The aim of the present work is to demonstrate a principally new approach
to the problem of the definition of the boundary condition at the open end of
the tube when the incoming wave is a pure sine with frequency corresponding to
the first linear resonance and the outcoming wave is unknown. An account of
interaction of those two oppositely directed waves leads to the modified
Burgers' equation for the initial sound wave. The method proposed allows one to
describe the latter wave by the same equation. The numerical analysis of this
equation by Adams' method and predictor-corrector scheme permits one to
calculate the unknown outcoming wave and to define the boundary condition at
the open end as a superposition of the incoming and outcoming waves. It is
shown that results obtained are in good agreement with those predicted by the
Sturtevant's experiment [B. Sturtevant, J. Fluid Mech. 63(1), 97--120 (1974)].