Perturbation Technique for the Study of Three-Dimensional Separation

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Abstract
The three-dimensional boundary-layer equations are studied close to separation and to a plane of symmetry. Perturbation about a one-dimensional parabolic flow field leads to a sequence of linear equations which have eigensolutions, the first of which satisfies a nonlinear equation. This first eigensolution contains all the important information about the skin friction, and by appropriate choice of the perturbation problem the skin friction is shown to satisfy a first order nonlinear wave equation. The characteristics of this equation are the skin-friction lines (surface stream lines), and their behavior is described close to separation. The description obtained is a global one (that is, not restricted to the neighborhood of a plane of symmetry) when the cross flow is small. The validity of the local solution is confirmed by a Goldstein-type coordinate expansion.

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