Is the von Kármán constant affected by sediment suspension?

Abstract

Is the von Kármán constant affected by sediment suspension? The presence of suspended sediment in channels and fluvial streams has been known for decades to affect turbulence transfer mechanism in sediment‐laden flows, and, therefore, the transport and fate of sediments that determine the bathymetry of natural water courses. This study explores the density stratification effects on the turbulent velocity profile and its impact on the transport of sediment. There is as yet no consensus in the scientific community on the effect of sediment suspension on the von Kármán parameter,κ. Two different theories based on the empirical log‐wake velocity profile are currently under debate: One supports a universal value ofκ = 0.41 and a strength of the wake, Π, that is affected by suspended sediment. The other suggests that both κ and Π could vary with suspended sediment. These different theories result in a conceptual problem regarding the effect of suspended sediment on κ, which has divided the research area. In this study, a new mixing length theory is proposed to describe theoretically the turbulent velocity profile. The analytical approach provides added insight defining κas a turbulent parameter which varies with the distance to the bed in sediment‐laden flows. The theory is compared with previous experimental data and simulations using ak‐εturbulence closure to the Reynolds averaged Navier Stokes equations model. The mixing length model indicates that the two contradictory theories incorporate the stratified flow effect into a different component of the log‐wake law. The results of this work show that the log‐wake fit with a reducedκ is the physically coherent approximation.