Shroud assemblies and methods for cooling gas turbine engine shrouds are provided. For example, a shroud assembly comprises a shroud segment having hot and cold side portions. The hot side portion faces a gas flow path, and the cold side portion faces a cooling fluid flow path. The shroud assembly further comprises a shroud hanger for mounting the shroud segment in the gas turbine engine. The shroud hanger includes a conduit for receipt of a flow of cooling fluid that defines an outlet configured for the flow of cooling fluid to exit the conduit substantially tangential to the cold side portion of the shroud segment. The shroud and shroud hanger together define an annular cavity that forms the cooling fluid flow path, and fluid exits a plurality of conduits defined in the shroud hanger into the cavity substantially tangential to the shroud cold side to cool the shroud cold side.