Scaling transitions in plane turbulent wall jets

In the fully developed region of a plane turbulent wall jet, the key jet parameters, including the jet velocity U m, jet half-width z 1/2 and wall shear stress ₀, follow the classical power-law scaling with the streamwise distance x: U m v / M 0 ∼ (xM 0 / v 2) − α, z 1/2 M 0 / v 2 ∼ (xM 0 / v 2) β and ₀ v 2 / (ρ M₀^2) ∼ (xM 0 / v 2) − χ, where M 0 is the source kinematic momentum flux, v is the coefficient of kinematic viscosity of fluid, ρ is the mass density of fluid and α, β and χ are the positive scaling exponents. We present a theoretical framework to determine these exponents. Our framework reveals that each jet parameter exhibits a scaling transition. This transition is driven by a shift in the scaling law of the skin-friction coefficient as the Reynolds number Re m = U m z m / v changes over from Re m 10 000, where z m is the wall-normal location corresponding to the jet velocity. Specifically, α transitions from 4 (1 + γ) / (9 − γ) to 13 (1 + γ) /2 (14 − γ), β from 8/ (9 − γ) to 13/ (14 − γ) and χ from (9 + 7 γ) / (9 − γ) to (14 + 12 γ) / (14 − γ), where γ ≈ 0. 05 is a parameter determined from experiments. We validate the theoretical predictions against extensive experimental datasets from the literature.