  We examine the behavior of the spectral function for the trace of the stress
tensor in QCD in the two regimes where it is possible to make analytical
progress; weak coupling, and close to a second order QCD phase transition. We
determine the behavior of the bulk viscosity in each regime. We discuss the
problem of analytic continuation of the (lattice) Euclidean correlation
function to determine the spectral function. In each case the spectral function
has a narrow peak at small frequency; its shape would be challenging to extract
accurately from lattice data with error bars.
