  We compute, in the framework of the fluid/gravity correspondence, the
transport coefficients of a relativistic fluid affected by chiral and
gauge-gravitational anomalies, including external electromagnetic fields. The
computation is performed at first and second order in the hydrodynamical
expansion. We use a 5-dim holographic model with pure gauge and mixed
gauge-gravitational Chern-Simons terms in the action. We reproduce at first
order previous results on the anomaly induced current of a magnetic field and a
vortex in a relativistic fluid, and compute at second order the anomalous and
non anomalous transport coefficients by using a Weyl covariant formalism. We
find a dissipative and anomalous correction to the chiral magnetic conductivity
due to the time dependence of the magnetic field. We also find a new
contribution from the mixed gauge-gravitational anomaly to the shear waves
dispersion relation. The role played by the chiral and gravitational anomalies
in other transport coefficients is discussed.
