A turbine section of a gas turbine engine, comprising: a stator assembly comprising an inner diameter end wall, an outer diameter end wall, and a stator vane extending between the inner diameter end wall and the outer diameter end wall within a mainstream gas flow path; a turbine rotor assembly downstream of the stator assembly and including a rotor blade extending into the mainstream gas flow path; a housing including an annular shroud that circumscribes the rotor blade and at least partially defines the mainstream hot gas flow path; a first baffle arranged to define a first cavity with the outer diameter end wall of the stator assembly; a second baffle; and a third baffle arranged to define a second cavity with the second baffle and a third cavity with the shroud; a fourth baffle within the second cavity; wherein the first cavity is fluidly coupled to the second cavity and the second cavity is fluidly coupled to the third cavity such that a first portion of a cooling air flows from the first cavity to the second cavity and from the second cavity to the third cavity, wherein the first baffle includes a first set of holes configured to direct said cooling air into the second cavity and to impinge said first portion of cooling air on an aft end of the outer diameter end wall, wherein the stator assembly includes an aft rail extending radially from the outer diameter end wall to the first baffle, and wherein the aft rail defines a second set of holes extending at least partially axially through the aft rail to fluidly couple the first cavity to the second cavity, wherein the first cavity is formed by a first sub-cavity proximate to a leading edge of the outer diameter end wall, a second sub-cavity proximate to the stator vane, and a third sub-cavity proximate to the aft end of the outer diameter end wall, wherein the first, second, and third sub-cavities (261, 262, 263) are fluidly isolated from one another, wherein the third baffle includes a third set of holes configured to direct the first portion of cooling air into the third cavity to impinge onto a radially outer surface of the shroud, and wherein each of the first baffle and the second baffle forms a respective seal with the aft rail, and the third baffle forms a seal with the aft rail and the fourth baffle. a stator assembly comprising an inner diameter end wall, an outer diameter end wall, and a stator vane extending between the inner diameter end wall and the outer diameter end wall within a mainstream gas flow path; a turbine rotor assembly downstream of the stator assembly and including a rotor blade extending into the mainstream gas flow path; a housing including an annular shroud that circumscribes the rotor blade and at least partially defines the mainstream hot gas flow path; a first baffle arranged to define a first cavity with the outer diameter end wall of the stator assembly; a second baffle; and a third baffle arranged to define a second cavity with the second baffle and a third cavity with the shroud; a fourth baffle within the second cavity; wherein the first cavity is fluidly coupled to the second cavity and the second cavity is fluidly coupled to the third cavity such that a first portion of a cooling air flows from the first cavity to the second cavity and from the second cavity to the third cavity, wherein the first baffle includes a first set of holes configured to direct said cooling air into the second cavity and to impinge said first portion of cooling air on an aft end of the outer diameter end wall, wherein the stator assembly includes an aft rail extending radially from the outer diameter end wall to the first baffle, and wherein the aft rail defines a second set of holes extending at least partially axially through the aft rail to fluidly couple the first cavity to the second cavity, wherein the first cavity is formed by a first sub-cavity proximate to a leading edge of the outer diameter end wall, a second sub-cavity proximate to the stator vane, and a third sub-cavity proximate to the aft end of the outer diameter end wall, wherein the first, second, and third sub-cavities (261, 262, 263) are fluidly isolated from one another, wherein the third baffle includes a third set of holes configured to direct the first portion of cooling air into the third cavity to impinge onto a radially outer surface of the shroud, and wherein each of the first baffle and the second baffle forms a respective seal with the aft rail, and the third baffle forms a seal with the aft rail and the fourth baffle.