A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non-lifting problems. The unique feature of the present theory is the consideration of the slow variation of the boundary layer thickness. The slowly varying behavior is treated by using the method of multi-time scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aero¬dynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow.
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