Unified scaling laws for turbulent boundary layers across flow regimes

TL;DR

This paper establishes unified scaling laws for turbulent boundary layers, accurately describing wall shear stress and velocity profiles across various flow regimes using local variables.

Contribution

It introduces a novel information-theoretic approach to identify minimal sets of dimensionless variables that predict flow behavior without assuming specific functional forms.

Findings

Two variables describe wall shear stress effectively.

Three variables characterize the mean velocity profile.

Scaling laws unify different flow regimes, collapsing data across conditions.

Abstract

We discover unified scaling laws for the mean wall shear stress and the mean velocity profile in turbulent boundary layers subject to favorable and adverse mean pressure gradients-including flows with separation and reattachment. We use the information-theoretic irreducible error theorem to identify, among all dimensionally consistent combinations, the dimensionless groups with maximal predictive power, without assuming any functional form. Two dimensionless variables suffice to describe the mean wall shear stress, while three characterize the mean velocity profile. The scaling laws depend exclusively on variables defined at a fixed streamwise location, demonstrating that judiciously chosen combinations of local quantities implicitly encode upstream history without requiring global parameters. The results are validated against a rich collection of cases and are shown to collapse mean quantities across flow regimes previously thought to require distinct treatments.