  Towards modelling the charge asymmetry observed in heavy ion collisions, we
present here analytic solutions of relativistic hydrodynamics containing parity
violating and anomalous terms at the first order in the hydrodynamic
approximation. These terms can induce chiral magnetic and chiral vortical
effect leading to the generation of the charge asymmetry. We also consider
sphaleron solutions with non trivial winding number to model the phenomenon. We
calculate the net chiral charge difference produced in our solutions. We
anticipate their relevance also in the context of baryogenesis in early
universe, neutron star and some condensed matter situations.
