Three-dimensional finite element simulation of acoustic propagation in spiral bubble net of humpback whale

In 2004, Leighton hypothesized that the acoustic calls emitted by humpback whales when feeding using bubble nets, may enhance the effectiveness of the net in confining prey (such as herring) by forming a "wall of sound" with a quiet zone within. Modelling of the acoustics of this phenomenon was previously restricted to 2D; this paper conducts a 3D model of the propagation of signals resembling those emitted by humpback whales when bubble netting, projected into an upward spiral bubble net which data to date suggest is the accurate form for the bubble net in 3D space. In this study, the feeding calls were analyzed in the time-frequency domain to extract acoustic information sufficient to allow modeling of the resulting spatial distribution of acoustic pressure and particle velocity, and how they vary over the duration of the call. Sound propagation in the bubble net was described by using a linear steady-state formulation for an effective medium of bubbly water. Using the predicted attenuation, phase velocity and density in bubbly water, a 3D finite element model was constructed to numerically simulate the upward-spiral bubble net which consists of a mixture of bubbles that exhibit a range of radii. The acoustic pressure field and particle motion field were both calculated within the bubble net. The simulation results show that the energy of the whale feeding call could be effectively focused in the bubble net, generating intensive sound pressure and particle motion fields in the bubbly arm of the net, but with some "quiet" regions closer to the center of the net, as Leighton hypothesized. Furthermore, when the hearing ability of herring is taken into consideration, the results suggest that this acoustic focusing effect could be a plausible factor in trapping them in the bubble net. It also allows speculation on the possible enhancements that the time-varying nature of the call during feeding could give to the whale in this mechanism for the bubble net feeding by humpback whales.