Summary of Work and Intellectual Merits Recent probabilistic descriptions of particle motions, borrowing key ideas from statistical mechanics, offer a compelling strategy for connecting statistical descriptions of particle motions with dynamical formulations of coupled fluid-particle behavior. The proposed work is aimed at adding this style of analysis to the discussion on bed load sediment transport, growing the connection between small-scale mechanistic descriptions of transport and larger-scale problems of morphodynamics and tracer motions. Ensembles and ensemble averaging. It is possible to describe essential features of flow and bed load particle motions to formally define an ensemble of particle configurations and velocities in a manner similar to (but not identical to) formulations from classic statistical mechanics. The proposed work will elaborate the idea of an ensemble and ensemble averaging for bed load transport to clarify important effects of active particle patchiness and nonuniform conditions associated with bedforms. The bed load sediment version of the Maxwell-Boltzmann distribution. Evidence from high-speed imaging of bed load particle motions and from momentum-based descriptions of particle motions indicates that the ensemble distribution of instantaneous particle velocities is exponential-like. The project will involve pursuing a theoretical formulation of this distribution from statistical-mechanics arguments. The relation between particle velocities and diffusivities. Whereas evidence for anomalous diffusion is compelling for tracer particle motions involving multiple hops with intervening rest times, diffusion at the timescale relevant to calculating the sediment flux is normal (Fickian). In addition, there is a clear theoretical basis for relating the particle diffusivity to the ensemble average particle velocity. The proposed work will pursue a set of physical and computational experiments designed to fully clarify this relationship. Computational analysis of coupled fluid-particle behavior. Our numerical sediment transport modeling system is the first discrete-particle transport model to have four-way coupling (mass and momentum exchange between the solids and fluid) and the ability to resolve turbulence structures. It is therefore is uniquely capable of exploring the detailed mutual interactions between turbulence structures and sediment motions. Computational analyses will go hand-in-hand with the theoretical and experimental parts of the work to clarify fluid-particle interactions that may not be observable in experiments. Mixed particle sizes. Building on the behavior of single particle sizes, the project will involve pursuing theoretical, experimental and computational work focused on the behavior of mixed sizes. Of particularly interested are the effects of covariance in particle activities and velocities in computing sediment fluxes, and the spatiotemporal organization of motions of mixed particle sizes in response to turbulence.
|Effective start/end date||9/1/12 → 1/31/17|
- National Science Foundation (NSF): $249,835.00