A system for a turbomachine includes a rotor blade configured to rotate along a circumferential direction within a casing of the turbomachine and a shroud positioned outward of the rotor blade along a radial direction. The rotor blade includes a root, a tip spaced radially outward from the root, a pressure side tip rail that extends around the tip of the rotor blade along a pressure side wall, and a suction side tip rail that extends around the tip of the rotor blade along a suction side wall. The shroud includes a radially inner surface facing the pressure side tip rail and the suction side tip rail of the rotor blade and spaced from the pressure side tip rail and the suction side tip rail of the rotor blade by a clearance gap. The shroud also includes a plurality of grooves extending continuously along the circumferential direction.