A unified algebraic turbulence closure for channel, pipe and boundary-layer flows: sub-percent errors against DNS and experimental data with a minimal set of inputs

<title>Abstract</title> <p>Classical turbulence closures for wall-bounded flows generally fail on three fronts simultaneously: they require many input parameters (6–15 constants), are calibrated for a single geometry (channel, pipe, or boundary layer) without transferring to others, and produce errors of several percent — or fail to converge — when solved using a single solver. This work follows an explicit equation-weighing methodology: Verify which classical models actually work when implemented with identical solvers and published constants. Extract the equations that are functional and validated. Apply new structural features measured from direct numerical simulations (DNS), including a Reynolds-number-dependent van Driest constant, geometry offsets, and a Reynolds-number-dependent Coles wake. Weigh each equation term by its impact on the total error. Rebuild the closure using only the highest-weight terms. Test it against 23 real datasets (DNS channels, Superpipe experiments, and DNS boundary layers). The resulting mixing-length closure has 12 calibrated constants, requires only 3 user inputs (geometry, Reynolds number, and fluid), and reproduces channels, pipes, and zero-pressure-gradient boundary layers with mean absolute errors of 0.55%, 0.54%, and 0.41%, respectively — achieving a combined error of 0.50%. This performance is five times lower than the best converging classical algebraic model (2.64%) and orders of magnitude below differential models, which fail to converge in the same framework. Leave-one-family-out blind tests show that the model generalizes to geometries unseen during calibration, extrapolates approximately one decade beyond the calibrated Reynolds range, and remains insensitive to grid size. Reducing the number of input parameters while simultaneously reducing the error is shown not to be a trade-off, but rather a direct cause of more reliable simulations.</p>