A study of degenerate and nondegenerate critical points in three-dimensional flow fields

Critical point theory is applied to incompressible flow. Degenerate critical points are emphasized. It is found that free-slip critical points (away from a no-slip boundary) are degenerate if the vorticity is finite. Such flows are found to be locally two-dimensional unless the flow is unsteady or the viscosity is finite. Viscous effects appear only in higher-order terms of the series expansion for velocity. They change the character of the first-order solution. No-slip critical points can have asymptotically exact nondegenerate first order solutions for the ratio of local flow velocity to normal distance from the wall.