  We present simulations of low-mass planet--disc interactions in inviscid
three-dimensional discs. We show that a wind-driven laminar accretion flow
through the surface layers of the disc does not significantly modify the
migration torque experienced by embedded planets. More importantly, we find
that 3D effects lead to a dramatic change in the behaviour of the dynamical
corotation torque compared to earlier 2D theory and simulations. Although it
was previously shown that the dynamical corotation torque could act to slow and
essentially stall the inward migration of a low-mass planet, our results in 3D
show that the dynamical corotation torque has the complete opposite effect and
speeds up inward migration. Our numerical experiments implicate buoyancy
resonances as the cause. These have two effects: (i) they exert a direct torque
on the planet, whose magnitude relative to the Lindblad torque is measured in
our simulations to be small; (ii) they torque the gas librating on horseshoe
orbits in the corotation region and drive evolution of its vortensity, leading
to the negative dynamical corotation torque. This indicates that at low
turbulent viscosity, the detailed vertical thermal structure of the
protoplanetary disc plays an important role in determining the migration
behaviour of embedded planets. If this result holds up under a more refined
treatment of disc thermal evolution, then it has important implications for
understanding the formation and early evolution of planetary systems.
