Induced leading-edge flow separation is critical to the formation of one-dimensionally stable positions in in-line schooling*

Stable positions, speed and propulsive efficiency benefits have all been found in the schooling of in-line swimmers. However, the mechanisms behind school cohesion and how the key variables of Lighthill number and dimensionless amplitude can modulate the cohesion and associated hydrodynamic benefits are not fully understood. Here new simulations of two purely pitching teardrop hydrofoils in an in-line arrangement are examined with a potential flow advanced boundary element method (ABEM) solver augmented by a leading-edge suction parameter based separation model.  The foils freely swim in the streamwise direction and have a fencing scheme to prevent penetration of the impinging wake vortex elements into the downstream hydrofoil. The ABEM solver is validated against a wide array of previous simulations and experiments. When leading-edge separation is suppressed it’s discovered that the follower always collides into the leader showing no school cohesion across a wide range of initial conditions, Lighthill numbers, and dimensionless amplitudes. When leading-edge separation is allowed, one-dimensionally stable arrangements form and agree with previous experiments. For swimmers in stable equilibrium arrangements increasing the Lighthill number not only makes them be spaced closer together, but also distorts the linear relationship between stable positions and the phase lag.