  The transport by materially coherent eddies is studied in a two-layer
quasigeostrophic model of geophysical turbulence. The coherent eddies are
identified by closed contours of the Lagrangian-averaged vorticity deviation
obtained from Lagrangian particles advected by the flow. A series of flow
regimes with different bottom friction strengths are considered---it is found
that coherent eddies become more prevalent and longer-lasting as the strength
of the bottom drag increases. These coherent eddies, with average core radius
close to the deformation radius, propagate zonally with speeds close to the
long baroclinic Rossby wave speed and meridionally with a preference for
cyclones to propagate poleward and anticyclones to propagate equatorward. The
meridional propagation preference of the coherent eddies gives rise to a
systematic upgradient potential vorticity (PV) transport, which is in the
opposite direction as the background PV transport and not captured by standard
Lagrangian diffusivity estimates. The upgradient PV transport by coherent eddy
cores is less than 10% of the total PV transport, but the PV transport by the
periphery flow induced by the PV inside coherent eddies is significant and
downgradient. This clarifies the distinct roles of the trapping and stirring
effect of coherent eddies in PV transport in geophysical turbulence.
