Higher-Order Boundary-Layer Equations
If locally the boundary-layer thickness is not small compared with the smallest radius of curvature of the surface, the pressure gradient normal to the surface - within the boundary layer - may no longer be small of higher order, and hence no longer be negligible. This is the best known higher-order effect. There are other higherorder effects, see e.g. van DYKE [ 6], but here only curvature effects are being considered and described by the addition of terms to the first-order boundary-layer equations (see chapter 2). The equations presented here have been derived by ROBERT [ 3], who evaluated separately the influence of wall curvature itself and the wall-curvature gradient, an approach which was found to be necessary by KUX [ 1]. No attempt is being made to review the numerous sets of governing equations (including the modeling of turbulence), which appeared in literature, and the corresponding methods to solve them.
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