Modeling the acoustic scattering from large fish schools using the Bloch-Floquet theorem

Scattering from large fish schools can significantly contribute to volume reverberation in the open ocean measured by mid-frequency long-range SONAR systems (1–10 kHz). This can potentially cause large false-alarms, especially if the resonance frequencies of the fish’ air-filled swim bladder is excited. Hence, to ultimately improve the detection performance of long-range SONAR systems, we seek an efficient modeling technique for the acoustic scattering created by large school of fish, which readily accounts for the fish bio-acoustic properties, school’s spatial configuration and multiple scattering effects. We exploit here a key observation to simplify our problem: fish in larger schools tend to swim in a periodic arrangement whereby we approximate the large school as an infinite system with a periodic collection of fish’ air filled swimbladders. Thus, the Bloch-Floquet theorem, governing waves in periodic media, allows predictions of the acoustic field in an infinite media by simply modeling the dynamic response of a single unit cell only (containing one fish). This approach allows one to rapidly predict the frequency dependent reflection and transmission coefficient on a semi-infinite fish school for various incident waves. Good agreement was found with the results obtained from finite element modeling of realistic, finite sized fish schools.