A method for operating a turbofan engine assembly including a core gas turbine engine is provided. The method includes varying an operating speed of the turbofan engine assembly from a first operating speed to a second operating speed. The method also includes selectively positioning a first arcuate portion and a second arcuate portion of a split cowl assembly to vary a throat area of a fan nozzle duct defined downstream from the core gas turbine engine to facilitate improving engine efficiency at the second operating speed. The split cowl assembly is downstream from the core gas turbine engine and inside the fan nozzle duct. A turbofan engine assembly and nozzle assembly are also provided.