A variable geometry assembly for modulating a fluid flow in a turbomachine is disclosed. The assembly comprises a first ring having a plurality of first wedge-shaped elements and having an axis, and a second ring having a plurality of second wedge-shaped elements and having an axis. The second ring is substantially coaxial to the first ring. The second wedge-shaped elements co-act with the first wedge-shaped elements. Flow passages are defined between pairs of sequentially arranged first wedge-shaped elements and second wedge-shaped elements. The first ring and the second ring are angularly displaceable one with respect to the other. Moreover, the first ring and the second ring are configured to move axially with respect to one another when the first ring and the second ring are angularly displaced one with respect to the other.