The pulsed flow about a circular non-centred orifice inside a cylindrical duct is analysed to obtain insight into the basic three-dimensional vortex dynamics that may be expected behind natural cardiac valves. The problem is approached by a high-resolution numerical simulation. Results show how a small finite eccentricity generates a fully three-dimensional vortex wake that evolves quite differently from that found under an axisymmetric approximation. The flow field is analysed in terms of velocity and vorticity fields. The vortex wake structure is that of an initially quasi-axisymmetric vortex ring that progressively deforms into a three-dimensional structure, and whose vortex lines tend to reconnect with the boundary-layer-induced vorticity. The vortex structure explains secondary circulation and the presence of a diastolic backflow jet localized behind the longer orifice edge, in agreement with previous experimental observations. Possible relevance of the results to flows of cardiovascular interest is discussed.