  We study the fluid dynamics of two fish-like bodies with synchronised
swimming patterns. Our studies are based on two-dimensional simulations of
viscous incompressible flows. We distinguish between motion patterns that are
externally imposed on the swimmers and self-propelled swimmers that learn
manoeuvres to achieve certain goals. Simulations of two rigid bodies executing
pre-specified motion indicate that flow-mediated interactions can lead to
substantial drag reduction and may even generate thrust intermittently. In turn
we examine two self-propelled swimmers arranged in a leader-follower
configuration, with a-priori specified body-deformations. We find that the
swimming of the leader remains largely unaffected, while the follower
experiences either an increase or decrease in swimming speed, depending on the
initial conditions. Finally, we consider a follower that synchronises its
motion so as to minimise its lateral deviations from the leader's path. The
leader employs a steady gait while the follower uses a reinforcement learning
algorithm to adapt its swimming-kinematics. We find that swimming in a
synchronised tandem can yield up to about 30% reduction in energy expenditure
for the follower, in addition to a 20% increase in its swimming-efficiency. The
present results indicate that synchronised swimming of two fish can be
energetically beneficial.
