Abstract. We present a new formulation of the bedload sediment flux probability distribution. Individual particles obey Langevin equations which are switched on and off by particle entrainment and deposition. The flux is calculated as the rate of many such particles crossing a control surface within a specified observation time. Flux distributions inherit observation-time dependence from the on-off motions of particles. At the longest observation times, distributions converge to sharp peaks around classically-expected values, but at short times, fluctuations are erratic. We relate this scale dependence of bedload transport rates to the movement characteristics of individual grains. This work provides a statistical mechanics description for the fluctuations and observation-scale dependence of sediment transport rates.

<p><span id="page27R_mcid3" class="markedContent"><span dir="ltr" role="presentation">Solute mixing is efficient in a steady three dimensional porous media flow,</span><span dir="ltr" role="presentation"> since filaments of solute elongate exponentially fast in time. This "chaotic"</span><span dir="ltr" role="presentation"> elongation enables molecular diffusion to </span><span dir="ltr" role="presentation">rapidly distribute solute concentrations. </span></span><span id="page27R_mcid3" class="markedContent"><span dir="ltr" role="presentation">In two dimensional steady flows, such as through thin fractures in rock, existing knowledge indicates that filaments of solu</span><span dir="ltr" role="presentation">te elongate much more slowly than exponentially, meaning the mixing is far less efficient. Here, we present experimental evidence that when porous media flows are instead unsteady, two dimensional mixing becomes chaotic.  Using 3D printed model porous media with steady longitudinal and oscillating transverse flow components, we measure Lyapunov exponents of filament elongation and quantify solute stretching and folding statistics as a function of the frequency and amplitude of the transverse flow. We find resonances in mixing frequency which are consistent with numerical simulations of the model geometry. These findings improve our understanding of mixing in geological systems and provide insights which may be useful to design efficient geologically-inspired mixing devices in the future.</span></span></p>

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<p>Bed load experiments reveal a range of possibilities for the downstream velocity distributions of moving particles, including normal, exponential, and gamma distributions. Although bed load velocities are key for understanding fluctuations in transport rates, existing models have not accounted for the full range of observations. Here, we present a generalized Langevin model of particle transport that includes turbulent drag and episodic particle-bed collisions. By means of analytical calculations, we demonstrate that momentum dissipation by particle-bed collisions controls the form of the bed load velocity distribution. As collisions vary between elastic and inelastic, the velocity distribution interpolates between normal and exponential. These results add context to conflicting experiments on bed load velocities and suggest that granular interactions regulate sediment dynamics and transport rate fluctuations.</p>

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