  In the cold dark matter model of structure formation, galaxies are assembled
hierarchically from mergers and the accretion of subclumps. This process is
expected to leave residual substructure in the Galactic dark halo, including
partially disrupted clumps and their associated tidal debris. We develop a
model for such halo substructure and study its implications for dark matter
(WIMP and axion) detection experiments. We combine the Press-Schechter model
for the distribution of halo subclump masses with N-body simulations of the
evolution and disruption of individual clumps as they orbit through the
evolving Galaxy to derive the probability that the Earth is passing through a
subclump or stream of a given density. Our results suggest that it is likely
that the local complement of dark matter particles includes a 1-5% contribution
from a single clump. The implications for dark matter detection experiments are
significant, since the disrupted clump is composed of a `cold' flow of
high-velocity particles. We describe the distinctive features due to halo
clumps that would be seen in the energy and angular spectra of detection
experiments. The annual modulation of these features would have a different
signature and phase from that for a smooth halo and, in principle, would allow
one to discern the direction of motion of the clump relative to the Galactic
center.
