Compliant bellow seal may be axially disposed between first and second cooling plates bounding first and second cooling passages between cooling plates and first and second stage disks in turbine. Bellow seal includes two or more convolutions with oppositely facing forward and aft sealing surfaces, which may be flat, on forward and aft annular sealing walls and cylindrical annular outer and inner contact and sealing surfaces on and facing radially outwardly or inwardly from one of the convolutions. A snake bellow seal embodiment may have at least two of the convolutions being full convolutions of unequal width and a forwardmost partial convolution including the sealing wall.Bellow seal may allow turbine cooling flow from an inter-stage radial face spline to flow through inner openings of second cooling passage and block first stage disk cooling air from flowing through inner openings of first cooling passage.