In standard accretion discs, outward angular momentum transfer by
viscous forces is compensated by the inward motion of the accreting
matter. However, the vertical structure of real accretion discs leads to
meridional circulation with comparable amplitudes of poloidal
velocities. Using thin-disc approximation, we consider different regimes
of disc accretion with different vertical viscosity scalings. We show
that, while gas-pressure-dominated discs can easily have a mid-plane
outflow, standard thin radiation-pressure-dominated disc is normally
moving inwards at all the heights. However, quasi-spherical scaling for
pressure (p ∝ ϖ^-5/2) leads to a mid-plane outflow
for a very broad range of parameters. In particular, this may lead to a
reversed, outward heat advection in geometrically thick discs when the
temperature decreases rapidly enough with height. While the overall
direction of heat advection depends on the unknown details of vertical
structure and viscosity mechanisms, existence of the mid-plane
counterflow in quasi-spherical flows is a robust result weakly dependent
on the parameters and the assumptions of the model. Future models of
thick radiatively inefficient flows should take meridional circulation
into account.