  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 for a general energy-momentum
tensor, include scalar, vector and tensor modes and extend some previous works
where matter was assumed to be a perfect fluid. Through a harmonic
decomposition, the system of equations is then transformed to evolution
equations in time and algebraic constraints. This result is then applied to
dissipative one-component fluids, and on using the simplified acausal Eckart
theory the system is reduced to two closed subsystems governed by four and
eight harmonic coefficients for the odd and even sectors respectively. The
system is also seen to close in a simplified causal theory. It is then
demonstrated, within the Eckart theory, how vorticity can be generated from
viscosity.
