Universal formula for incipient sediment motion in turbulent flows
Abstract
Sediment is among the leading pollutant in rivers and streams across the world. Despite a century of research, describing sediment concentration in streams and how sediments are initiated into motion remains a formidable challenge and continues to draw significant research attention. The reason this problem remains daunting is that it requires the description of incipient motion of grains by complex eddying (or turbulent) motion, a topic that has resisted complete theoretical treatment to date. This is also a topic that has many science clienteles and thus draws attention in erosion studies, river bank stability, ecosystem sciences, food web modeling, eolian processes, and space sciences including the reconstruction of a number of surface features on Mars and Titan. Upon combining several data sources, an empirical diagram between a densimetric Froude number at which incipient sediment motion occurs and relative roughness was recently reported in the literature for over some 6 decades of grain sizes. This data became the obvious test- bed for new theories aiming to describe sediment transport over a wide range of grain sizes and flow conditions. A recently published theory proposed that the origin of some of the intermediate scaling laws of sediment transport are related to different mechanisms of how eddies transfer their energy across scales. This theory requires the existence of an inverse cascade of energy (i.e. energy flows from small to large eddies) when the sediment diameter is small, which contradicts studies of energy transfer over smooth boundaries. Moreover, a unified theory that describes the entire shape of this data set for all grain sizes remains elusive. In this talk, a theory that relates the sediment incipient motion to the turbulence properties near the surface of the sediments is covered. The model features a derivation using a cospectral budget (CSB) approach that mathematically describes how eddies of different sizes contribute to the overall turbulent stress experienced by sediments. The CSB model is promising as the presence of a questionable inverse cascade is no longer required. The work bridges three separate concepts: the universal character of the forward energy cascade in turbulent eddies near surfaces, the pressure-velocity redistribution properties, and the force balance on grains.
- Publication:
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AGU Fall Meeting Abstracts
- Pub Date:
- December 2020
- Bibcode:
- 2020AGUFMEP0520031L
- Keywords:
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- 0439 Ecosystems;
- structure and dynamics;
- BIOGEOSCIENCES;
- 0481 Restoration;
- BIOGEOSCIENCES;
- 1825 Geomorphology: fluvial;
- HYDROLOGY;
- 4327 Resilience;
- NATURAL HAZARDS