Resonant oscillations of a gas in an open-ended tube

The reported investigation is concerned with the oscillations near resonance induced in a gas contained in a tube that is open at one end and has an oscillating piston at the other. It is shown that there are discontinuities in the oscillations within a certain frequency band near resonance, if all dissipative processes are disregarded. The modifying effects of a number of dissipative mechanisms are also investigated, taking into account compressive viscosity, damping arising from radiation at the open end, the effect of the boundary layer at the wall of the tube, and nonlinear dissipation such as might arise from eddy formation when separation occurs at the sharp lip of the open end. The main role of the first two mechanisms is to replace the discontinuities by sharp transitions and, more importantly, to determine their position. Under certain conditions it is possible for the boundary-layer effect to dominate the oscillations, which then differ substantially from those predicted by inviscid theory.