  Based on a holographic model incorporating both chiral anomaly and
gravitational anomaly, we study the effect of magneto-vortical coupling on
transport properties of a strongly coupled plasma. The focus of present work is
on the generation of a vector charge density and an axial current, as response
to vorticity in a magnetized plasma. The transport coefficients parameterising
the vector charge density and axial current are calculated both analytically
(in the weak magnetic field limit) and also numerically (for general values of
the magnetic field). We find the generation of vector charge receives both
non-anomalous and anomalous contributions, with the non-anomalous contribution
dominating in the limit of strong magnetic field and the anomalous contribution
sensitive to both chiral anomaly and gravitational anomaly. On the contrary, we
find the axial current is induced entirely due to the gravitational anomaly,
thus we interpret the axial current generation as chiral vortical effect. The
corresponding chiral vortical conductivity is found to be suppressed by the
magnetic field. By Onsager relation, these transport coefficients are
responsible for the generation of a thermal current due to a transverse
electric field or a transverse axial magnetic field, which we call thermal Hall
effect and thermal axial magnetic effect, respectively.
