Discontinuous Potential Flow as the Limiting Form of the Viscous Flow for Vanishing Viscosity

抄録

The asymptotic behaviour of the viscous flow past an obstacle for vanishingly small viscosity is discussed on the basis of Prandtl’s boundary layer theory together with Kirchhoff’s dead water theory. If the pressure distribution around the obstacle is such that the separation of the boundary layer on the obstacle takes place, then the flow pattern should involve free stream-lines extending from the separation points. From such considerations it is concluded that the asymptotic flow pattern around a smooth obstacle is a discontinuous flow with dead water region of the Kirchhoff type such that the free stream-lines leave the obstacle with a finite curvature equal to that of the obstacle at the separation point.