  We extend our recent study of chiral magnetic effect in relativistic heavy
ion collisions based on an anomalous transport model by including also the
chiral vortical effect. We find that although vorticities in the chirally
restored quark matter, which result from the large angular momentum in
non-central collisions, can generate an axial charge dipole moment in the
transverse plane of a heavy ion collision, it does not produce a difference in
the eccentricities of negatively and positively charged particles. As a result,
including the chiral vortical effect alone cannot lead to a splitting between
the elliptic flows of negatively and positively charged particles. On the other
hand, negatively and positively charged particles do develop a splitting in
their elliptic flows if the effect due to a strong and long-lived magnetic
field is also included. However, to have a positive slope in the dependence of
the elliptic flow splitting on the charge asymmetry of the quark matter, as
seen in experiments, requires the neglect of the effect of the Lorentz force.
In this case, an elliptic flow splitting appears even at vanishing charge
asymmetry.
