  Motivated by numerically modeling surface waves for inviscid Euler equations,
we analyze linear models for damped water waves and establish decay properties
for the energy for sufficiently regular initial configurations. Our findings
give the explicit decay rates for the energy, but do not address
reflection/transmission of waves at the interface of the damping. Still for a
subset of the models considered, this represents the first result proving the
decay of the energy of the surface wave models.
