I. Eigenmotion analysis

Abstract

General wedge and comer problems lead to the introduction of complex Navier-Stokes equations of complex laminar motions the real parts of which describe real laminar flows. Under the non-slip condition at the surface of a dihedral angle the general solution of the complex Navier-Stokes equations is established on the basis of the corresponding integral of the Stokes equations of slow motions. The latter integration is accomplished in terms of slow-motion eigenfunctions with real and complex eigenvalues. The results render valuable information about the flow properties at the leading or trailing edge of a dihedral angle. Weakly singular solutions, which are characterized by an infinite pressure and a finite velocity at the edge of the dihedral angle, are shown to exist for all wedges under asymmetric attack and for sharp wedges under symmetric attack. The existence of critical and branching eigenvalues exhibits the non-analyticity of laminar flows around dihedral angles in their dependence upon the corresponding wedge or corner angles.