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
$J_T(x)$ (non-dimensionalized by its inlet value) as a function of the streamwise distance
$x$, we prove that
$J_T(x) >1$ – 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
$J_T>1$), which yields scaling laws for key jet measures: the mean streamwise and transverse velocities
$U(x,y)$ and
$V(x,y)$, the turbulence intensities, the Reynolds shear stress
$-\rho \,\overline {u'v'}(x,y)$, the mean pressure
$P(x,y)$, etc. Experiments satisfying
$J_T(x)>1$ validate our predictions for all jet measures, including, among others, the profiles of
$U$,
$V$ and
$-\rho \,\overline {u'v'}$. We further predict
$U \sim x^{-0.24}$,
$V \sim x^{-0.45}$,
$-\rho \,\overline {u'v'}\sim x^{-0.69}$, the mass flux
$Q_m \sim x^{0.55}$, and
$J_T$ increases to approximately 1.5. Contrary to the classical linear jet spread, we find sublinear spread, with the jet half-width growing like
$b(x)\sim x^{0.79}$, 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.