Transient Anomalous Diffusion and Advective Slowdown of Bedload Tracers by Particle Burial and Exhumation

摘要

The process of burial and exhumation of bedload particles within a certain depth of the riverbed leads to vertical exchange of particles, which significantly affects the characteristics of streamwise bedload transport. In this paper, we revisit the classic active layer formulation and extend it by incorporating the burial and exhumation through conceptualizing the fluctuations of bed surface as the relative vertical movement of buried tracer particles in the substrate layer (i.e., we change the static reference system to the fluctuating riverbed surface). We theoretically demonstrate, for the first time, the emergence of the transient anomalous diffusion (both superdiffusion and subdiffusion) and power-law advective slowdown at the intermediate timescales, which are induced by the nonequilibrium transport as characterized by the inhomogeneous vertical mixing of tracers due to particle burial and exhumation. Neglecting the ballistic regime at extremely short times, at small and large timescales, the transport regimes show normal diffusion. This result further implies that for the most typical fluvial riverbed with finite vertical exchange depth (i.e. nonaggrading or nondegrading bed), the subdiffusion of bedload tracers for large timescale transport may still be transient, which will eventually converge to the normal diffusion as time increases. Comparing the obtained analytical solutions with available numerical results as well as field observations, we show that the proposed formulation can capture well anomalous diffusion and the power-law slowdown of the advective velocity of bedload tracers at intermediate timescales, and more importantly the transition from anomalous to normal diffusion at large timescales.