Turbulent Poiseuille Flow Modelling by an Enhanced Prandtl-Driest Mixing Length

The turbulent Poiseuille flow between two parallel plates is one of the simplest possible physical situations, and it has been studied intensively. Different mixing lengths are used, but no one, to the best of our knowledge, has simultaneously considered the boundary conditions of two walls together with damping effects from both walls. In this paper, we propose an enhanced Prandtl-Driest mixing length that not only satisfies all of the boundary conditions, but it also includes both walls' damping effects as well. With our new formulations, we numerically solve the problem and, moreover, propose an explicit approximate solution. As applications of our solutions, the total velocity, total shear stress, energy dissipation density, energy balance, Kolmogorov scale law, and friction of turbulent Poiseuille flow are studied in detail. The study discovers that the high heels profiles of both mean and total velocity are universal for all wall-bounded turbulent flows.