Effects of phase difference on hydrodynamic interactions and wake patterns in high-density fish schools

In this study, we numerically investigate the effects of the tail-beat phase differences between the trailing fish and its neighboring fish on the hydrodynamic performance and wake dynamics in a two-dimensional high-density school. Foils undulating with a wavy-like motion are employed to mimic swimming fish. The phase difference varies from 0[Formula: see text] to 360[Formula: see text]. A sharp-interface immersed boundary method is used to simulate flows over the fish-like bodies and provide quantitative analysis of the hydrodynamic performance and wakes of the school. It is found that the highest net thrust and swimming efficiency can be reached at the same time in the fish school with a phase difference of 180[Formula: see text]. In particular, when the phase difference is 90[Formula: see text], the trailing fish achieves the highest efficiency, 58% enhancement compared with a single fish, while it has the highest thrust production, increased by 108% over a single fish, at a phase difference of 0[Formula: see text]. The performance and flow visualization results suggest that the phase of the trailing fish in the dense school can be controlled to improve thrust and propulsive efficiency, and these improvements occur through the hydrodynamic interactions with the vortices shed by the neighboring fish and the channel formed by the side fish. In addition, the investigation of the phase difference effects on the wake dynamics of schools performed in this work represents the first study in which the wake patterns for systems consisting of multiple undulating bodies are categorized. In particular, a reversed Bénard–von Kármán vortex wake is generated by the trailing fish in the school with a phase difference of 90[Formula: see text], while a Bénard–von Kármán vortex wake is produced when the phase difference is 0[Formula: see text]. Results have revealed that the wake patterns are critical to predicting the hydrodynamic performance of a fish school and are highly dependent on the phase difference.