--> Abstract: Incorporating Stochastic Sediment Transport Models in Time-Resolved Numerical Models of Turbulent Flows in Rivers, by Mark W. Schmeeckle, David J. Furbish, Jonathan M. Nelson, and Ryosuke Akahori; #90078 (2008)

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Incorporating Stochastic Sediment Transport Models in Time-Resolved Numerical Models of Turbulent Flows in Rivers

Mark W. Schmeeckle1, David J. Furbish2, Jonathan M. Nelson3, and Ryosuke Akahori4
1School of Geographical Sciences, Arizona State University, Tempe, AZ
2Department of Earth & Environmental Sciences, Vanderbilt University, Nashville, TN
3Geomorphology and Sediment Transport Laboratory, US Geological Survey, Golden, CO
4Kobe University, Kobe, Japan

Deterministic, time-resolved simulations of turbulence are increasingly common in river and marine flows. We present one such Large Eddy Simulation (LES) model for flows in rivers. However, current sediment transport models are lacking in similar sophistication and do not account for the temporal and spatial distribution of modeled turbulence structure. Our previous work has shown that these elements are critical to physics-based modeling of sedimentary bedforms. In river and marine flows the smallest turbulence length scales are much larger than the molecular length scales of the fluid, and the continuum approximation is valid. However, the number density of sediment grains is rarely large enough to justify this continuum assumption, and the velocity and position of sediment should be regarded as a stochastic process. We present stochastic models for bedload and suspended sediment transport.

For suspended sediment we derive Langevin equations for particle simulations that are coupled to our LES model of flow in rivers. The Langevin equations include a deterministic component of displacement related to the modeled fluid velocity and the particle settling velocity, as well as a stochastic component of displacement related to the subgrid stress.

Bedload grains undergo frequent collisions with the bed during transport and are also entrained and deposited in response to near-bed turbulent fluctuations of the fluid velocity. These factors contribute to a broad probability density function of bedload grain velocity, particularly at low transport stages. We derive a Fokker-Planck sediment transport equation and a probabilistic Exner equation for the change in bed elevation with time. This formulation of the erosion equation includes an advective and dispersive flux term. We derive parameters for the stochastic bedload model using high-speed video experiments.

 

AAPG Search and Discover Article #90078©2008 AAPG Annual Convention, San Antonio, Texas