A turbine ring sector is disclosed. The turbine ring sector includes a wall bounding an aerodynamic flowpath in which gases flow from the upstream region toward the downstream region, and a multiperforated plate, situated on the opposite side of the aerodynamic flowpath with respect to the wall. The multiperforated plate includes a bottom and side walls. The distance between the wall of the ring sector and the bottom of the multiperforated plate defines a gap which is progressive in an axial direction, from the upstream region toward the downstream region. The value of the gap situated at the upstream region is below the value of the gap situated at the downstream region.