A contoured turbine airfoil assembly including an end wall (30a) formed by platforms (30) located circumferentially adjacent to each other, and a row of airfoils (34a, 34b) integrally joined to the end wall (30a) and spaced laterally apart to define flow passages (46) therebetween for channeling gases in an axial direction. A trough (62) is defined between a pressure side ridge (48) and a suction side ridge (58) located forward of each pair of airfoils (34a, 34b). Each trough (62) has a direction of elongation aligned to direct flow into the flow passage (46) centrally between each pair of airfoils (34a, 34b).