Nuclei at very high energy, characterized by a saturation scale, can be described by an effective theory of Quantum ChromoDynamics (QCD) called Color Glass Condensates. The earliest phase of the collision of two nuclei is modeled as the collision of two sheets of color glass. The classical field resulting from the collision then decays and equilibrates to a plasma of quarks and gluons. Using a recursive solution of the Yang-Mills equations, we calculate analytic expressions for the gluon field created in ultra-relativistic heavy ion collisions at small times ?. We have worked out explicit solutions for the fields and the energy momentum tensor up to 4^th order in an expansion in ? . We generalize the existing calculations to go beyond the limit of large homogenous nuclei. This allows us to calculate radial and elliptic flow of gluon fields. The resulting transverse and longitudinal structure of the Poynting vector field has a rich phenomenology. Besides the well known radial and elliptic flow in transverse direction, classical quantum chromodynamics predicts a rapidity-odd transverse flow that tilts the fireball for non-central collisions, and it implies a characteristic flow pattern for collisions of non-symmetric systems A + B. The rapidity-odd transverse flow translates into a directed particle flow v_1 which has been observed at RHIC and LHC. The global flow fields in heavy ion collisions could be a powerful check for the validity of classical Yang-Mill dynamics in high energy collisions. We also propose a procedure to calculate the energy momentum tensor of gluon fields on an event-by-event basis. The matching of the initial field energy momentum tensor to viscous hydrodynamic initial conditions is discussed and some preliminary results of a subsequent hydrodynamic evolution are shown. Our results can provide event-by-event initial conditions for hydrodynamic simulations of nuclear collisions that include initial flow and initial shear stress.
