  We calculate the diurnal and annual modulation of the signals in axion and
WIMP dark matter detectors on Earth caused by a cold flow of dark matter in the
Solar neighborhood. The effects of the Sun's and the Earth's gravity, and of
the orbital and rotational motions of the Earth are included. A cold flow on
Earth produces a peak in the spectrum of microwave photons in cavity detectors
of dark matter axions, and a plateau in the nuclear recoil energy spectrum in
WIMP detectors. Formulas are given for the positions and heights of these peaks
and plateaux as a function of time in the course of day and year, including all
corrections down to the 0.1% level of precision. The results can be applied to
an arbitrary dark matter velocity distribution $f(\vec{v})$ by integrating the
one-flow results over velocities. We apply them to the set of flows predicted
by the caustic ring model of the Galactic halo. The caustic ring model predicts
the dark matter flux on Earth to be largest in December $\pm$ one month.
Nonetheless, because of the role of energy thresholds, the model is consistent
with the annual modulation results published by the DAMA collaboration provided
the WIMP mass is larger than approximately 100 GeV.
