  Explicit expressions are found for the axisymmetric metric perturbations of
the closed, flat and open FRW universes caused by toroidal motions of the
cosmic fluid. The perturbations are decomposed in vector spherical harmonics on
2-spheres, but the radial dependence is left general. Solutions for general
odd-parity $l$-pole perturbations are given for either angular velocities or
angular momenta prescribed. In particular, in case of closed universes the
solutions require a special treatment of the Legendre equation.
