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A nonlinear perturbation problem for steady two-dimensional inviscid transonic flow with a local supersonic region is considered. A damping condition is prescribed on a portion of the boundary in order to prevent the arising of shock waves in the flow. The existence of a smooth solution to the problem is established. A proof is based on the Fredholm alternative and on a technique for uniqueness analysis worked out by and Cook (1978).2000 Mathematics Subject Classification: 35M10, 76H05.

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A turbulent flow past two symmetric airfoils, whose bow and aft portions are circular arcs, whereas midparts are flat, is studies numerically. The amplitude of lift coefficient oscillations versus the free-stream Mach number M ∞ is analyzed at zero angle of attack. Ranges of M ∞ in which there exist flow bifurcations are determined.