  We formulate the chiral vortical effect (CVE) and its generalization called
generalized vortical effect using the semiclassical theory of wave packet
dynamics. We take the spin-vorticity coupling into account and calculate the
transport charge current by subtracting the magnetization one from the Noether
local one. We find that the transport charge current in the CVE always vanishes
in relativistic chiral fermions. This result implies that it cannot be observed
in transport experiments in condensed matter systems such as Dirac/Weyl
semimetals with the pseudo-Lorentz symmetry. We also demonstrate that the
anisotropic CVE can be observed in nonrelativistic systems that belong to the
point groups $D_n, C_n (n = 2, 3, 4, 6)$, and $C_1$, such as $n$-type
tellurium.
