  The hydrodynamic description of transversally thermalized matter, possibly
formed at the early stages of ultra-relativistic heavy-ion collisions, is
developed. The formalism is based on the thermodynamically consistent approach
with all thermodynamic variables referring to two-dimensional objects, the
so-called transverse clusters, which are identified with the particles having
the same rapidity. The resulting hydrodynamic equations for a single cluster
have the form of the two-dimensional hydrodynamic equations of the perfect
fluid. Since the clusters do not perform any work in the longitudinal
direction, their energy is completely transformed and used to generate strong
radial and elliptic flows that turn out to be compatible with the experimental
data.
