A rotating detonation combustor includes a combustion chamber configured for a rotating detonation process to produce a flow of combustion gas and an air plenum configured to contain a volume of air. The rotating detonation combustor also includes a flow passage coupled in flow communication between the combustion chamber and the air plenum and configured to channel an airflow from the air plenum. The rotating detonation combustor also includes a fuel inlet coupled in flow communication with the flow passage and configured to channel a fuel flow into the flow passage. The flow passage includes a plurality of fuel mixing mechanisms configured to mix the airflow and the fuel flow within the combustion chamber.