  We employ a model system, called rowers, as a generic physical framework to
define the problem of the coordinated motion of cilia (the metachronal wave) as
a far from equilibrium process. Rowers are active (two-state) oscillators
interacting solely through forces of hydrodynamic origin. In this work, we
consider the case of fully deterministic dynamics, find analytical solutions of
the equation of motion in the long wavelength (continuum) limit, and
investigate numerically the short wavelength limit. We prove the existence of
metachronal waves below a characteristic wavelength. Such waves are unstable
and become stable only if the sign of the coupling is reversed. We also find
that with normal hydrodynamic interaction the metachronal pattern has the form
of stable trains of traveling wave packets sustained by the onset of
anti-coordinated beating of consecutive rowers.
