Turbulent jet theory via Lie symmetry analysis: The free plane jet

A theory of incompressible turbulent plane jets (TPJs) is proposed by advancing an improved boundary layer approximation over the limiting classical - retaining more terms in the momentum balance equations. A pressure deficit inside the jet (with respect to the ambient) must exist due to transverse turbulence (Miller & Comings, J. Fluid Mech., vol. 3, 1957, pp. 1-16; Hussain & Clarke, Phys. Fluids, vol. 20, 1977, pp. 1416-1426). Contrary to the universally accepted invariance of the total momentum flux (non-dimensionalized by its inlet value) as a function of the streamwise distance, we prove that 1$]]> - a condition that all TPJs must satisfy; surprisingly, prior theories and most experiments do not satisfy this condition. This motivated us to apply Lie symmetry analysis with translational and dilatational transformations of the modified equations (incorporating 1$]]>), which yields scaling laws for key jet measures: the mean streamwise and transverse velocities and, the turbulence intensities, the Reynolds shear stress, the mean pressure, etc. Experiments satisfying 1$]]> validate our predictions for all jet measures, including, among others, the profiles of, and. We further predict, the mass flux, and increases to approximately 1.5. Contrary to the classical linear jet spread, we find sublinear spread, with the jet half-width growing like, indicating a narrower jet. Our predictions differ notably from most results reported in the literature. These contradictions demand revisiting jet studies involving carefully designed facilities and boundary conditions, and highly resolved simulations.