  Metachronal swimming, the sequential beating of limbs with a small phase lag,
is observed in many organisms at various scales, but has been studied mostly in
the limits of high or low Reynolds numbers. Motivated by the swimming of brine
shrimp, a mesoscale organism that operates at intermediate Reynolds numbers, we
computationally studied a simple nonreciprocal 2D model that performs
metachronal swimming. Our swimmer is composed of two pairs of paddles beating
with a phase difference that are symmetrically attached to the sides of a flat
body. We numerically solved the Navier-Stokes equations and used the immersed
boundary method to model the interactions between the fluid and swimmer. To
investigate the effect of inertia and geometry, we performed simulations
varying the paddle spacing and the Reynolds numbers in the range $Re = 0.05 -
100$. In all cases, we observed back-and-forth motion during the cycle and a
finite cycle-averaged swim speed at steady state. Interestingly, we found that
the swim speed of the swimmer has nonmonotonic dependence on $Re$, with a
maximum around $Re\approx1$, a flat minimum between $Re=20-30$ and an eventual
increase for $Re>35$. To get more insight into the mechanism behind this
relationship, we first decomposed the swim stroke of the swimmer and each
paddle into power and recovery strokes and characterized the forward and
backward motion. Unlike for reciprocal swimmers, here, for parts of the cycle
there is competition between the two strokes of the paddles - the balance of
which leads to net motion. We then studied the cycle-averaged, as well as,
power-stroke-averaged and recovery-stroke-averaged fluid flows, and related
differences in the fluid field to the nonmonotonic behavior of the swim speed.
Our results suggest the existence of distinct motility mechanisms that develop
as inertia increases within the intermediate-Re range.
