  We investigate the properties of the hydrodynamic flow around eccentric
protoplanets and compare them with the often assumed case of a circular orbit.
To this end, we perform a set of 3D hydrodynamic simulations of protoplanets
with small eccentricities ($e\leq 0.1$). We adopt an isothermal equation of
state and concentrate resolution on the protoplanet to investigate flows down
to the scale of the protoplanet's circumplanetary disk (CPD). We find enhanced
prograde rotation exterior to the CPD for low planet masses undergoing subsonic
eccentric motion. If the eccentricity is made large enough to develop a bow
shock, this trend reverses and rotation becomes increasingly retrograde. The
instantaneous eccentric flow field is dramatically altered compared to circular
orbits. Whereas the latter exhibit a generic pattern of polar inflow and
midplane outflow, the flow geometry depends on orbital phase in the eccentric
case. For even the modest eccentricities tested here, the dominant source of
inflow can come from the midplane instead of the poles. We find that the amount
of inflow and outflow increases for higher $e$ and lower protoplanet masses,
thereby recycling more gas through the planet's Bondi radius. These increased
fluxes may increase the pebble accretion rate for eccentric planets up to
several times that of the circular orbit rate. In response to eccentric motion,
the structure and rotation of the planet's bound CPD remains unchanged. Because
the CPD regulates the eventual accretion of gas onto the planet, we predict
little change to the gas accretion rates between eccentric and circular
planets.
