  The infall of cold dark matter onto a galaxy produces cold collisionless
flows and caustics in its halo. If a signal is found in the cavity detector of
dark matter axions, the flows will be readily apparent as peaks in the energy
spectrum of photons from axion conversion, allowing the densities, velocity
vectors and velocity dispersions of the flows to be determined. We discuss the
evolution of velocity dispersion along cold collisionless flows in one and two
dimensions. A technique is presented for obtaining the leading behaviour of the
velocity dispersion near caustics. The results are used to derive an upper
limit on the energy dispersion of the Big Flow from the sharpness of its nearby
caustic, and a prediction for the dispersions in its velocity components.
