A cooling system for a turbine engine is provided. The turbine engine includes a compressor, a compressor discharge chamber (CDC), a combustor assembly, and a turbine coupled in a serial flow relationship such that a first portion of air from the CDC is channeled to the combustor assembly. The turbine is coupled to the compressor via a rotor. The cooling system includes an air duct configured to channel a second portion of air from the CDC to a mid-rotor region of the rotor, and a fluid supply system coupled to the air duct at a coupling. The fluid supply system is configured to channel a flow of fluid to the coupling. The coupling is configured to cool the second portion of CDC air via absorption of heat by the fluid from the second portion of CDC air.