An airfoil is provided for a turbine of a gas turbine engine. The airfoil comprises: an outer structure comprising a first wall including a leading edge, a trailing edge, a pressure side, and a suction side; an inner structure comprising a second wall spaced from the first wall and at least one intermediate wall; and structure extending between the first and second walls so as to define first and second gaps between the first and second walls. The second wall and the at least one intermediate wall define at least one pressure side supply cavity and at least one suction side supply cavity. The second wall may include at least one first opening near the leading edge of the first wall. The first opening may extend from the at least one pressure side supply cavity to the first gap. The second wall may further comprise at least one second opening near the trailing edge of the outer structure. The second opening may extend from the at least one suction side supply cavity to the second gap. The first wall may comprise at least one first exit opening extending from the first gap through the pressure side of the first wall and at least one second exit opening extending from the second gap through the suction side of the second wall.