Qualitative analysis of mode transitions in bottle-shaped resonators with waterfall plots

A closed bottle-shaped resonator consists of the coupled neck and cavity. Such a system yields avoided crossings where the resonance of the neck matches that of the cavity when one bottle dimension is varied. Self-sustained oscillations within the bottle are generated thermoacoustically. Mode transitions were previously observed to occur at the same position within a few millimeters when a piston controlled with a translation stage was moved with a manual control to adjust the cavity length. The dominant mode was recorded using a power spectrum of the signal measured with a pressure sensor. In this study, the piston motion is automated and eight neck/cavity combinations were tested at three different piston speeds and at various input powers. The input powers were adjusted to just above thermoacoustic onset and not to exceed thermal limits of the materials used. Waterfall plots allow the visualization of the time evolution of the power spectrum where intensity is plotted both as a function of time and frequency. Qualitatively, the transitions occur at the same place within the cavity after a threshold input power is reached. Interestingly, overtones appear in most cases to be harmonics of the fundamental with either all or only odd harmonics present.