Labyrinth seal for a turbine engine of an aircraft

A labyrinth seal for a turbine engine, comprising a rotor element rotating about an axis of rotation, and a stator element extending around the rotor element, the rotor element comprising a series of annular lip(s) extending radially outwards and surrounded by at least one abradable element carried by the stator element, each lip comprising an inner peripheral body portion, an outer peripheral body portion and an upstream annular face for impact of an air flow during operation, at least one lip having, looking from said upstream annular face, a first annular cavity with a concave rounded cross-section on its inner peripheral body portion and a second annular cavity with a concave rounded cross-section on its outer peripheral body portion, said at least one lip having its inner peripheral body portion which has symmetry in relation to a median plane substantially perpendicular to said axis of rotation, wherein said second cavity extends from said upstream annular face in the downstream direction, and passes through said median plane.