Hydrodynamic interactions and wake dynamics of fish schooling in rectangle and diamond formations

The study is motivated by the quest to understand hydrodynamic interactions and wake dynamics of fish schooling. Using the constraint immersed boundary method, the work numerically investigates multiple 1-DoF self-propelled fish swimming in two-dimensional rectangle and diamond formations at different spacing. A comprehensive analysis on the hydrodynamic performance and wake dynamics of the formation is conducted. The result indicates that three stable formations of fish schools can be observed, including the rectangle, side-by-side and staggered formations. The in-phase rectangle formation at large spacing is more beneficial to the swimming efficiency of each individual in the school. The research also presents that the disorganized wake could lead to a very low chance for constructive regular vortex interaction and steady hydrodynamic benefit. Conversely, the steady formation could lead to a higher chance for an organized wake structure. Meanwhile, the work seeks to understand further hydrodynamic interaction mechanisms in collective swimming by considering the pressure field. In the staggered formation, the interaction of body-fitted pressure regions along the diagonal can maximize the thrust improvement of the trailing fish. An alternative hypothesis for optimally efficient locomotion is proposed. The study could offer some new insights into understanding collective behaviors of aquatic organisms.