Swimming performance and vorticity structures of a mother–calf pair of fish

• Flow over two foils with different arrangements and kinematics has been simulated.
• We find that both mother and calf fish benefit in tandem and staggered arrangements.
• Both fish can get better performance by changing their phase difference and velocity.

Flow around two foils of different sizes is investigated by solving the incompressible Navier–Stokes equations numerically with a space-time finite element method to study the swimming performance and vorticity structures of a mother–calf pair of fish. Based on simulations over a wide range of the relative position, Reynolds number, phase difference and phase velocity between the foils, we discuss in detail the drag coefficient, hydrodynamic power, root-mean-square value of the lift, and vorticity structures. It is found that both the mother and calf fish benefit in tandem and staggered arrangements. By changing their phase difference and phase velocity, the fish can get better performance in terms of thrust increase and hydrodynamic power saving. The mechanism of these strategies which are used to improve the performance is enhancing a reverse Kármán street or diminishing a Kármán street.