An assembly comprises a first cooling cavity disposed within one or more of a turbine assembly or a combustion chamber of an engine. The first cooling cavity directs cooling air within the one or more of the turbine assembly or the combustion chamber. The assembly comprises a second cooling cavity also disposed within the one or more of the turbine assembly or the combustion chamber. The second cooling cavity receives at least some of the cooling air from the first cooling cavity. A forward facing step nozzle forms a channel that fluidly couples the first cooling cavity with the second cooling cavity. The step nozzle includes steps having elongated first sides and narrow second sides. The elongated first sides of the steps protrude into the channel such that a cross-sectional area of the channel of the step nozzle at the steps is smaller than a cross-sectional area of the channel of the step nozzle outside of the steps.