  Migration of giant planets in discs with low viscosity has been studied
recently. The proportionality between migration speed and the disc's viscosity
is broken by the presence of vortices that appear at the edges of the
planet-induced gap. Our goal is to investigate vortex-driven migration in
low-viscosity discs in the presence of radial advection of gas, as expected
from angular momentum removal by magnetised disc winds. We performed three
dimensional simulations using the grid-based code FARGOCA. We mimicked the
effects of a disc wind by applying a synthetic torque on a surface layer of the
disc characterised by a prescribed column density Sigma_A so that it results in
a disc accretion rate of 10^-8 Solar masses per year. Discs with this structure
are called 'layered' and the layer where the torque is applied is denoted as
'active'. We also consider the case of accretion focussed near the disc
midplane to mimic transport properties induced by a large Hall effect or by
weak Ohmic diffusion. We observe two migration phases: in the first phase, the
migration of the planet is driven by the vortex and is directed inwards. This
phase ends when the vortex disappear. Migration depends on the ability of the
torque from the planet to block the accretion flow. When the flow is fast and
unimpeded (small Sigma_A) migration is very slow. When the accretion flow is
completely blocked, migration is faster and the speed is controlled by the rate
at which the accretion flow refills the gap behind the migrating planet. The
migration speed of a giant planet in a layered protoplanetary disc depends on
the thickness of the accreting layer. The lack of large-scale migration
apparently experienced by the majority of giant exoplanets can be explained if
the accreting layer is sufficiently thin to allow unimpeded accretion through
the disc.
