Potential energy of air bubbles in glacier ice and its conversion into acoustic energy

Air bubbles in glacier ice are released into the water and may generate sound as the ice melts. A major missing link in the study of this sound is an estimate of the sound energy radiated per unit of ice that melts. We present a theoretical upper bound for the sound energy that can be produced by the bubbles by computing their acoustically available potential energy. A more stringent upper bound based on a simple model for the behavior of the bubble upon release from the ice is then developed. These theory and model-based estimates are then compared to the results of experiments conducted with glacial ice collected from Hornsund Fjord, Svalbard. We find that the acoustic energy radiated by the melting ice in these experiments is less than the potential energy and the modeled maximum energy. However, we also find that there is substantial variability in the sound generated by the ice that is not explained by differences in the potential energy of the bubbles. We present some evidence that suggests this is a result of variation in the way in which individual bubbles are released, with bubbles that escape rapidly generating more sound than those that escape gradually.