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In this paper, small perturbations of a non-uniform two-dimensional flow of a compressible inviscid fluid are considered. It is shown that for a particular class of main stream Mach number distributions, which are characterized by a sonic line along the x-axis, the linearized shear flow equation may be transformed into the generalized Tricomi equation. The mixed boundary value problem which results from considering perturbations generated by a two-dimensional camber surface is formulated and solved by utilizing the Wiener-Hopf technique.

Airfoil in a sonic shear flow jet: a mixed boundary value problem for the generalized Tricomi equation