  GJ1214b is a warm sub-Neptune transiting in front of a nearby M dwarf star.
Recent observations indicate the presence of high and thick clouds or haze
whose presence requires strong atmospheric mixing. In order to understand the
transport and distribution of such clouds/haze, we study the atmospheric
circulation and the vertical mixing of GJ1214b with a 3D General Circulation
Model for cloud-free hydrogen-dominated atmospheres (metallicity of 1, 10 and
100 times the solar value) and for a water-dominated atmosphere. We analyze the
effect of the atmospheric metallicity on the thermal structure and zonal winds.
We also analyze the zonal mean meridional circulation and show that it
corresponds to an anti-Hadley circulation in most of the atmosphere with
upwelling at mid-latitude and downwelling at the equator in average. This
circulation must be present on a large range of synchronously rotating
exoplanets with strong impact on cloud formation and distribution. Using simple
tracers, we show that vertical winds on GJ1214b can be strong enough to loft
micrometric particles and that the anti-Hadley circulation leads to a minimum
of tracers at the equator. We find that the strength of the vertical mixing
increases with metallicity. We derive 1D equivalent eddy diffusion coefficients
and find simple parametrizations from Kzz=7x10^2xP_{bar}^{-0.4} m^2/s for solar
metallicity to Kzz=3x10^3xP_{bar}^{-0.4} m^2/s for the 100xsolar metallicity.
These values should favor an efficient formation of photochemical haze in the
upper atmosphere of GJ1214b.
