Boundary Layer Development Derived from First Principles - Galilei Symmetry Group

Previously, we have analytically derived and numerically simulated the statistical development of the round turbulent jet, from the jet exit and across the self-similar region based on the fundamental assumption of the existence of the Galilei Symmetry Group and a constant density Newtonian fluid. Hence, we are not implementing the equations governing fluid flow, but instead basic symmetries that translate directly to the relevant conservation laws through Nöther’s theorem. The only inputs required using this methodology are the initial flow statistics (e.g. the initial mean velocity profile), which will vary between different flow generators, and the kinematic turbulent (eddy) viscosity, which specify how the viscous and turbulent diffusion affect the development of the flow. Herein, we extended to pipe flow boundary layers and flat plate zero pressure gradient boundary layers. The recursive program yields directly the relevant differential equation, simply from physical reasoning, leading to an analytical solution to the mean velocity profile in each case. The relevant differential equations describe the diffusion of momentum, similarly to the heat conduction equation describing the diffusion of heat. A control volume analysis of each respective flow describes the momentum diffusion due to internal shear forces. The agreement with experimental data is excellent.