  We present high-resolution hydrodynamical simulations of the degree and
direction of polarisation imprinted on the CMB by the Sunyaev-Zel'dovich effect
in the the line of sight to massive galaxy clusters. We focus on two
contributions which contribute most of the induced CMB polarisation in addition
to the intrinsic CMB quadrupole: the radiation quadrupole seen by electrons due
to their own velocity in the plane normal to the line of sight, and the
radiation quadrupole due to the thermal Sunyaev-Zel'dovich effect, which is
generated by a previous scattering elsewhere in the cores of the local and
nearby clusters. We show that inside the virial radius of a massive cluster,
this latter effect, although being second order in the optical depth, can reach
the level of the former effect. These two effects can, respectively, constrain
the projected tangential velocity and inner density profile of the gas, if they
can be separated with multi-frequency observations. As the information on the
tangential velocity of the ICM gas is combined with the kinetic
Sunyaev-Zel'dovich temperature effect probing the projected radial velocity it
will be possible to constrain the dynamics of the ICM. In particular, future
polarisation observations may be able to trace out the filamentary structure of
the cooler and less dense ionized gas that has not yet been incorporated into
massive clusters. We also discuss how the collapse of a cluster should produce
a peculiar ring-like polarisation pattern which would open a new window to
detect proto-clusters at high redshift.
