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We study the process of a galaxy moving through the intercluster gas in a cluster of galaxies, using a high quality hydrocode run at high resolutions. We find that ram pressure strippingoccurs in the form of individual events that are separated by about ten million years. In addition we find that the galaxy accretes gas from the downstream side into the core. This accretion process exhibits a radial "pumping" mode, similar to the one found previously in simulations of wind accretion onto compact objects. Some implications of our results for the understanding of a few recent observations are discussed.