  First order perturbations of homogeneous and hypersurface orthogonal LRS
(Locally Rotationally Symmetric) class II cosmologies with a cosmological
constant are considered in the framework of the 1+1+2 covariant decomposition
of spacetime. The perturbations, which are of perfect fluid type, include
general scalar, vector and tensor modes and extend some previous works where
vorticity perturbations were excluded.
  A harmonic decomposition is performed and the field equations are then
reduced to a set of eight evolution equations for eight harmonic coefficients,
representing perturbations in density, shear, vorticity and the Weyl tensor, in
terms of which all other variables can be expressed algebraically. This system
decouples into two sub-systems, one for five and one for three coefficients. As
previously known, vorticity perturbations cannot be generated to any order in a
barytopic perfect fluid. Hence the time development of existing first order
vorticity perturbations are seen to be completely determined by the background.
However, an already existing vorticity will act as source terms in the
evolution equations for the other quantities.
  In the high frequency approximation the four independent Weyl tensor
harmonics evolve as gravitational waves on the anisotropic background in the
same manner as in the case without vorticity, whereas vorticity gives a first
order disturbance of sonic waves.
