Heavy‐tailed travel distance in gravel bed transport: An exploratory enquiry

Bed load transport, where particles move intermittently in frequent contact with the bed, is the dominant mode of particle transport in gravel bed rivers and streams. Complex fluid/particle and particle/particle interactions lead to a broad distribution of transport behaviors under the same set of flow conditions. In this paper, we investigate the plausibility of heavy‐tailed movements for particles in bed load transport using carefully controlled flume experiments and theoretical analysis. In our experimental setting, we find travel distances for particles of a given size follow an exponential distribution whose mean varies with grain size. Building on previous work of Stark et al. (2009), we then develop a probability model to show how heavy‐tailed distributions of travel distance can emerge from a mixture of particle sizes. Heavy‐tailed travel distance can lead to anomalous diffusion in bed load transport, modeled by fractional derivatives in the transport equation.