Near and far field development of the turbulent round jet derived from Galilean symmetry

Based on the fundamental assumption of the existence of the Galilean Symmetry Group and a constant density Newtonian fluid, we have derived the average statistical properties of the free round turbulent jet. Using a small, recursive program that can conveniently run on a laptop and knowledge about the jet exit conditions, we can numerically predict the mean velocity profile all the way from the jet exit to beyond the self-similar region. We can also predict the jet spreading angle, entrainment and transverse velocity component and we can show the influence of Reynolds number and turbulent dynamic viscosity on the jet properties. From the knowledge gained from the recursive program or simply physical reasoning, we can derive a second order partial differential equation that describes the momentum diffusion. Solution of this equation by the Lie method gives us an analytical solution to the mean velocity profile. To cover both the region very close to the jet exit, the intermediate developing region and the far self-similar region, we have made careful measurements on three jets of different sizes with highly similar jet exit conditions: 10 mm, 50 mm and 100 mm diameter by means of hot-wire and laser anemometry. We find excellent agreement between measurements and theory, as well as with the numerical results, The measurements, the recursive computer program and the analytical solution all agree very well and illustrate how momentum diffusion is the governing process in the development of the mean velocity profile of the free jet at high Reynolds number. The results also illustrate the importance of the initial turbulent structure and the value of the turbulent kinematic viscosity on the far field spreading angle of the jet. The results also confirm that the mean properties of the jet are rather independent of the jet Reynolds number. Our investigation illustrates how basic properties of space and time asserts a profound influence on how “free flows” develop from their initial form and eventually assumes their final equilibrium state.