The present disclosure is directed to a gas turbine engine defining a longitudinal direction, a radial direction extended from an axial centerline, and a circumferential direction. The gas turbine engine includes a compressor section, a combustion section, and a turbine section in serial flow arrangement along the longitudinal direction. The gas turbine engine includes a low speed turbine rotor including a hub extended along the longitudinal direction and radially within the combustion section; a high speed turbine rotor including a high pressure (HP) shaft coupling the high speed turbine rotor to a HP compressor in the compressor section; and a first turbine bearing disposed radially between the hub of the low speed turbine rotor and the HP shaft. The HP shaft extends along the longitudinal direction and radially within the hub of the low speed turbine rotor. The high speed turbine rotor defines a turbine cooling conduit extended within the high speed turbine rotor. The first turbine bearing defines an outer air bearing along an outer diameter of the first turbine bearing and adjacent to the hub of the low speed turbine rotor. The first turbine bearing defines an inner air bearing along an inner diameter of the first turbine bearing and adjacent to the HP shaft. The first turbine bearing further defines a cooling orifice adjacent along the longitudinal direction to the turbine cooling conduit of the high speed turbine rotor. The cooling orifice and the turbine cooling conduit are in fluid communication.