Epithelial cells flows are observed both in vivo and in vitro and are essential for morphogenesis. Here, we show that pulsatile flows involving local contraction and expansion of a tissue can arise in vitro in an epithelial monolayer of Madine Darby Canine Kidney (MDCK) cells. The strength of pulsation can be modulated through friction heterogeneity by observing the monolayer dynamics on micro-contact printed fibronectin grids with dimensions matching the length-scale of spontaneous oscillations. We also report pulsations by inducing wound closure in domains of similar size with micro-fabricated pillars. In contrast, strongly coherent flows can be induced by adding and washing out acto-myosin cytoskeleton inhibitors. To gain insight into the associated cellular mechanisms, we fluorescently label actin and myosin. We find that lamellipodia align with the direction of the flow, and tissue-scale myosin gradients arise during pulsations in wound-healing experiments. Pulsations and flows are recapitulated in silico by a vertex model with cell motility and polarisation dynamics. The nature of collective movements depends on the interplay between velocity alignment and random diffusion of cell polarisation. When they are comparable, a significant pulsatile flow emerges, whereas the tissue undergoes long-range flows when alignment dominates. We conjecture that the interplay between lamellipodial motile activity and cell polarization, with a possible additional role for tissue-scale myosin gradients, is at the origin of the pulsatile nature of the collective flow. Altogether, our study reveals that monolayer dynamics is dictated by simple rules of interaction at cellular levels which could be involved in morphogenesis.