A turbulent boundary layer under an adverse pressure gradient doesn't just respond to the local pressure gradient — it remembers the pressure gradients it has encountered upstream. Two flows with identical local conditions but different histories produce different velocity profiles. This history effect is what makes adverse-pressure-gradient flows notoriously difficult to model.
The paper on composite mean velocity profiles for APG boundary layers (arXiv: 2603.23912) constructs a profile with three physically meaningful parameters, determined by nonlinear curve fitting to compiled datasets. One parameter captures pressure-gradient history effects in the wake region — the outer part of the boundary layer where the flow transitions to the freestream.
The formulation includes a velocity-overshoot function in the inner region and a reformulated wake function using a physically motivated boundary-layer thickness definition. Together, these modifications produce a composite profile that identifies well-behaved APG flows and quantifies how strongly the pressure-gradient history affects the current state.
A practical consequence: the framework enables reliable estimation of friction velocity and boundary-layer thickness when direct measurement is unavailable. And a fundamental finding: the von Kármán coefficient — the slope of the log law, debated for decades — approaches an invariant value of approximately 0.39 at sufficiently high Reynolds numbers, independent of the pressure gradient.
The through-claim: the log law is not invalidated by adverse pressure gradients — it's decorated by them. The universal structure (the logarithmic region with an invariant slope) persists; the non-universal structure (the wake, the overshoot, the history effects) organizes around it. Parameterizing the deviations reveals the invariance underneath.
2603.23912. Fluid dynamics / turbulent boundary layers / adverse pressure gradient / mean velocity profile / von Kármán coefficient.