Further consideration of the effect of curvature on the stability of three-dimensional flows

The effects of curvature on flow transitions is analyzed by means of solutions of boundary-layer equations for a yawed cylinder derived in the Cartesian coordinate system. The stability equations without expressions for surface curvature are expressed with the eigenvalue formulation by Malik (1982), and the temporal stability calculations are then derived for the case of curvature. The stability equations are set forth in an orthogonal curvilinear coordinate system both with and without in-plane and surface curvature terms. Calculations are presented for a yawed circular cylinder showing that in the absence of curvature the results are consistent with those of Cebeci and Stewartson (1980) and of Malik. When curvature is incorporated, however, the present calculating predict a small curvature effect which gradually diminishes at higher values of Re. The effect of curvature on transition is concluded to be smaller than other predictions indicate.