Numerical calculations are presented for the incompressible flow over a parabolic cylinder. Cylinder radii, smaller than the Tollmien-Schlichting wavelength of the boundary-layer flow, and smaller than those examined in previous studies, are considered. The calculation includes the flow upstream of the body, as well as the leading-edge region itself, and extends downstream into the region where the Blasius boundary-layer solution holds. A steady mean flow solution is computed and the results for the scaled surface vorticity and the displacement thickness are compared to previous studies. The unsteady problem is then formulated as a perturbation solution starting with and evolving from the mean flow. Comparisons are made with the Stokes wave solutions at various periods and locations within the boundary-layer. In the initial phase of this study reported here, these mean flow results are used to analyze some of the features observed in previous forced flow numerical studies.

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