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1. Generalization of Hop Distance‐Time Scaling and Particle Velocity Distributions via a Two‐Regime Formalism of Bedload Particle Motions

   https://doi.org/10.1029/2019WR025116  

   Wu, Zi ; Furbish, David ; Foufoula‐Georgiou, Efi ( January 2020 , Water Resources Research)

   To date, there is no consensus on the probability distribution of particle velocities during bedload transport, with some studies suggesting an exponential‐like distribution while others a Gaussian‐like distribution. Yet, the form of this distribution is key for the determination of sediment flux and the dispersion characteristics of tracers in rivers. Combining theoretical analysis of the Fokker‐Planck equation for particle motions, numerical simulations of the corresponding Langevin equation, and measurements of motion in high‐speed imagery from particle‐tracking experiments, we examine the statistics of bedload particle trajectories, revealing a two‐regime distance‐time (L‐T_p) scaling for the particle hops (measured from start to stop). We show that particles of short hop distances scale asL~giving rise to the Weibull‐like front of the hop distance distribution, while particles of long hop distances transition to a different scaling regime ofL~T_pleading to the exponential‐like tail of the hop distance distribution. By demonstrating that the predominance of mostly long hop particles results in a Gaussian‐like velocity distribution, while a mixture of both short and long hop distance particles leads to an exponential‐like velocity distribution, we argue that the form of the probability distribution of particle velocities can depend on the physical environment within which particle transport occurs, explaining and unifying disparate views on particle velocity statistics reported in the literature.

    

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2. A Statistical Description of Particle Motion and Rest Regimes in Open‐Channel Flows Under Low Bedload Transport

   https://doi.org/10.1029/2019JF005140  

   Liu, M. X. ; Pelosi, A. ; Guala, M. ( November 2019 , Journal of Geophysical Research: Earth Surface)

   In the last decade several efforts were devoted to model sediment‐particle transport in rivers as a stochastic process. Experimental observations are therefore needed to validate these models and to provide the correct probability distribution of selected stochastic variables. The kinematics of sand particles is investigated here using nonintrusive imaging to provide a statistical description of bedload transport under incipient motion conditions. In particular, we focus on the alternation between motion (particle steps) and rest regimes to quantify the probabilistic distribution of the particles waiting time, which is suggested by many studies to be responsible for anomalous diffusion. The probability distributions of the particle step time and step length, streamwise and spanwise velocities, acceleration, and waiting time are quantified experimentally. Results suggest that variables describing the particle motion regime are thin‐tailed distributed, whereas the waiting times exhibit a power law distribution. A specific class of waiting times during which the grain is observed to oscillate without a net displacement is classified as active and is analyzed separately from the other, so‐called deep waiting times. The experimental results, obtained under five different transport conditions, describe grain‐scale kinematics and dynamics at different wall shear stress. They provide both a benchmark data set for validating particle‐transport numerical simulation and critical input parameters for the stochastic modeling of bedload transport.

    

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3. Probability Distributions of Particle Hop Distance and Travel Time Over Equilibrium Mobile Bedforms

   https://doi.org/10.1029/2020JF005647  

   Ashley, Thomas C. ; Mahon, Robert C. ; Naqshband, Suleyman ; Leary, Kate C. P. ; McElroy, Brandon ( July 2020 , Journal of Geophysical Research: Earth Surface)

   The joint probability distribution of streamwise particle hop distance, lateral particle hop distance, and travel time constrains the relationships between topographic change and sediment transport at the granular scale. Previous studies have investigated the ensemble characteristics of particle motions over plane bed topography; however, it is unclear whether reported distributions remain valid when bedforms are present. Here, we present measurements of particle motion over bedform topography obtained in a laboratory flume and compare these to particle motions over plane bed topography with otherwise similar conditions. We find substantial differences in particle motion in the presence of bedforms that are relevant to macroscopic models of sediment transport. Most notably, bedforms increase the standard deviation of streamwise and lateral hop distances relative to the mean streamwise hop distance. This implies that bedforms increase the streamwise and lateral diffusion lengths and, equivalently, increase diffusive‐like fluxes.

    

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4. Comparison of quasi-geostrophic, hybrid and 3-D models of planetary core convection

   https://doi.org/10.1093/gji/ggac141  

   Barrois, O. ; Gastine, T. ; Finlay, C. C. ( April 2022 , Geophysical Journal International)

   We present investigations of rapidly rotating convection in a thick spherical shell geometry relevant to planetary cores, comparing results from quasi-geostrophic (QG), 3-D and hybrid QG-3D models. The 170 reported calculations span Ekman numbers, Ek, between 10−4 and 10−10, Rayleigh numbers, Ra, between 2 and 150 times supercritical and Prandtl numbers, Pr, between 10 and 10−2. The default boundary conditions are no-slip at both the ICB and the CMB for the velocity field, with fixed temperatures at the ICB and the CMB. Cases driven by both homogeneous and inhomogeneous CMB heat flux patterns are also explored, the latter including lateral variations, as measured by Q*, the peak-to-peak amplitude of the pattern divided by its mean, taking values up to 5. The QG model is based on the open-source pizza code. We extend this in a hybrid approach to include the temperature field on a 3-D grid. In general, we find convection is dominated by zonal jets at mid-depths in the shell, with thermal Rossby waves prominent close to the outer boundary when the driving is weaker. For the thick spherical shell geometry studied here the hybrid method is best suited for studying convection at modest forcing, $Ra \le 10 \, Ra_c$ when Pr = 1, and departs from the 3-D model results at higher Ra, displaying systematically lower heat transport characterized by lower Nusselt and Reynolds numbers. We find that the lack of equatorially-antisymmetric motions and z-correlations between temperature and velocity in the buoyancy force contributes to the weaker flows in the hybrid formulation. On the other hand, the QG models yield broadly similar results to the 3-D models, for the specific aspect ratio and range of Rayleigh numbers explored here. We cannot point to major disagreements between these two data sets at Pr ≥ 0.1, with the QG model effectively more strongly driven than the hybrid case due to its cylindrically averaged thermal boundary conditions. When Pr is decreased, the range of agreement between the hybrid and 3-D models expands, for example up to $Ra \le 15 \, Ra_c$ at Pr = 0.1, indicating the hybrid method may be better suited to study convection in the low Pr regime. We thus observe a transition between two regimes: (i) at Pr ≥ 0.1 the QG and 3-D models agree in the studied range of Ra/Rac while the hybrid model fails when $Ra\gt 15\, Ra_c$ and (ii) at Pr = 0.01 the QG and 3-D models disagree for $Ra\gt 10\, Ra_c$ while the hybrid and 3-D models agree fairly well up to $Ra \sim 20\, Ra_c$. Models that include laterally varying heat flux at the outer boundary reproduce regional convection patterns that compare well with those found in similarly forced 3-D models. Previously proposed scaling laws for rapidly rotating convection are tested; our simulations are overall well described by a triple balance between Coriolis, inertia and Archimedean forces with the length-scale of the convection following the diffusion-free Rhines-scaling. The magnitude of Pr affects the number and the size of the jets with larger structures obtained at lower Pr. Higher velocities and lower heat transport are seen on decreasing Pr with the scaling behaviour of the convective velocity displaying a strong dependence on Pr. This study is an intermediate step towards a hybrid model of core convection also including 3-D magnetic effects.

    

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5. Spatiotemporal bedload transport patterns over two-dimensional bedforms

   https://doi.org/10.5194/esurf-11-835-2023  

   Leary, Kate C. ; Tevis, Leah ; Schmeeckle, Mark ( September 2023 , Earth Surface Dynamics)

   Abstract. Despite a rich history of studies investigating fluid dynamics over bedforms and dunes in rivers, the spatiotemporal patterns of sub-bedform bedload transport remain poorly understood. Previous experiments assessing the effects of flow separation on downstream fluid turbulent structures and bedload transport suggest that localized, intermittent, high-magnitude transport events (i.e., permeable splat events) play an important role in both downstream and cross-stream bedload transport near flow reattachment. Here, we report results from flume experiments that assess the combined effects of flow separation–reattachment and flow re-acceleration over fixed two-dimensional bedforms (1.7 cm high; 30 cm long). A high-speed camera observed bedload transport along the entirety of the bedform at 250 frames per second. Grain trajectories, grain velocities, and grain transport directions were acquired from bedload images using semiautomated particle-tracking techniques. Downstream and vertical fluid velocities were measured 3 mm above the bed using laser Doppler velocimetry (LDV) at 15 distances along the bedform profile. Mean downstream fluid velocity increases nonlinearly with increasing distance along the bedform. However, observed bedload transport increases linearly with increasing distance along the bedform, except at the crest of the bedform, where both mean downstream fluid velocity and bedload transport decrease substantially. Bedload transport time series and manual particle-tracking data show a zone of high-magnitude, cross-stream transport near flow reattachment, suggesting that permeable splat events play an essential role in the region downstream of flow reattachment.

    

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