Abstract: A turbine nozzle includes an array of turbine vanes between inner and outer bands. Each vane includes opposed pressure and suction sides extending between opposed leading and trailing edges. The vanes define a plurality of flow passages each of which is bounded between the inner band, the outer band, and adjacent first and second vanes. A surface of the inner band in each of the passages is contoured in a non-axisymmetric shape including a peak of relatively higher radial height adjoining the pressure side of the first vane adjacent its leading edge, and a trough of relatively lower radial height is disposed parallel to and spaced-away from the suction side of the second vane aft of its leading edge. The peak and trough define cooperatively define an arcuate channel extending axially along the inner band between the first and second vanes.