Abstract

In this paper, we considered the well-known parabolic velocity field of Poiseuille flow, as a Riemannian manifold. Calculations of both first and second fundamental forms allowed mean and Gauss curvatures of the paraboloid of revolution, to be calculated. From the Lamb form of Navier-Stokes equation, we calculated both the flexion product and enstrophy giving the Lamb vector divergence as a function of Gauss curvature of the laminar velocity field. These results allowed the stability of Poiseuille flow to be investigated through the influence of maximum flow curvature and the Lamb vector divergence. We showed that classical critical Reynolds number approach is not enough to explain the change from laminar to transition flow regime. A new method, based on Gauss curvature calculation of the Riemannian manifold is then proposed.