Turbulent diffusion of momentum and suspended particles: A finite-mixing-length theory

A finite-mixing-length theory is presented for turbulent mixing. This theory contains Fickian diffusion as the limiting case for lm/L→0, where lm is the mixing length and L is the scale of the distribution under consideration. The new model is of similar generality to that of Taylor (1921), “Diffusion by continuous movements.” However, while Taylor’s model, being strictly Lagrangian, is difficult to apply to inhomogeneous scenarios, the new model is Eulerian and easily applicable to bottom boundary layers and other inhomogeneous flows. When applied to steady suspended sediment concentrations c(z), the theory predicts the observed trend of apparent Fickian diffusivities eFick=−wsc/(dc/dz) being larger for particles with larger settling velocity ws, in a given flow. The corresponding nature of the ratios between apparent Fickian sediment diffusivities and eddy viscosities, β=eFick/vt, for different particles in the same flow, is also revealed. That is, β is an increasing function of the particle settling ve...