Shedding some light on b-factors

The use of a Fickian (infinitesimal–mixing–length) framework for the case of turbulent mixing can necessitate the use of ad hoc modifications (e.g. β–factors) in order to reconcile experimental data with theoretical expectations. This is because in many cases turbulent mixing occurs on scales which cannot be considered infinitesimal. In response to this problem a Finite–Mixing– Length (FML) model for turbulent mixing was derived by Nielsen and Teakle. This paper considers the application of this model to the scenario of suspended sediment in steady, uniform channel flows. It is shown that, unlike the Fickian framework, the FML model is capable of explaining why β– factors are required to be an increasing function of ws/u*. The FML model does not on its own explain observations of β < 1, seen in some flat–bed experiments. However, some potential reasons for β < 1 are considered.