We discuss the energy flow of the classical gluon fields created in collisions of heavy nuclei at collider energies. We show how the Yang-Mills analoga of Faradays Law and Gauss Law predict the initial gluon flux tubes to expand or bend. The resultin
g 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.
Using a recursive solution of the Yang-Mills equation, we calculate analytic expressions for the gluon fields created in ultra-relativistic heavy ion collisions at small times $tau$. We have worked out explicit solutions for the fields and the energy
momentum tensor up to 4th order in an expansion in $tau$. We generalize the McLerran-Venugopalan model to allow for a systematic treatment of averaged charge densities $mu^2$ that vary as a function of transverse coordinates. This allows us to calculate radial, elliptic and directed flow of gluon fields. Our results can serve as initial conditions for hydrodynamic simulations of nuclear collisions that include initial flow.
