Molecular and atomic interactions of hydrogen on dust grains covered with ice at low temperatures are key mechanisms for star formation and chemistry in dark interstellar clouds. We have experimentally studied the interaction of atomic and molecular deuterium on nonporous amorphous water ice surfaces between 8 and 30 K, in conditions compatible with an extrapolation to an astrophysical context. The adsorption energy of D(2) presents a wide distribution, as already observed on porous water ice surfaces. At low coverage, the sticking coefficient of D(2) increases linearly with the number of deuterium molecules already adsorbed on the surface. Recombination of atomic D occurs via a prompt reaction that releases molecules into the gas phase. Part of the newly formed molecules are in vibrationally excited states (v=1-7). The atomic recombination efficiency increases with the presence of D(2) molecules already adsorbed on the water ice, probably because these increase the sticking coefficient of the atoms, as in the case of incident D(2). We have measured the atomic recombination efficiency in the presence of already absorbed D(2), as it is expected to occur in the interstellar medium. The recombination efficiency decreases rapidly with increasing temperature and is zero at 13 K. This allows us to estimate an upper limit to the value of the atom adsorption energy E(a) approximately 29 meV, in agreement with previous calculations.