[1] We introduce a new conceptual model for longitudinal and transverse diffusion of moving bed particles under weak bed load transport. For both rolling/sliding and saltating modes the model suggests that the particle motion is diffusive and comprises at least three ranges of temporal and spatial scales with different diffusion regimes: (1) the local range (ballistic diffusion), (2) the intermediate range (normal or anomalous diffusion), and (3) the global range (subdiffusion). The local range corresponds to ballistic particle trajectories between two successive collisions with the static bed particles. The intermediate range corresponds to particle trajectories between two successive periods of rest. These trajectories consist of many local trajectories and may include tens or hundreds of collisions with the bed. The global range of scales corresponds to particle trajectories consisting of many intermediate trajectories, just as intermediate trajectories consist of many local trajectories. Our data from the Balmoral Canal (the intermediate range) and Drake et al. 's [1988] data from the Duck Creek (the global range) provide strong support for this conceptual model and identify anomalous diffusion regimes for the intermediate range (superdiffusion) and the global range (subdiffusion).

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The vortex shedding topology of a heavy pendulum oscillating in a dense fluid is investigated using time-resolved three-dimensional particle tracking velocimetry (tr-3-D-PTV). A series of experiments with eight different solid to fluid mass ratios $m^*$ in the range $[1.14, 14.95]$ and corresponding Reynolds numbers of up to $Re \sim O(10^4)$ was conducted. The period of oscillation depends heavily on $m^*$ . The relation between amplitude decay and oscillation frequency is non-monotonic, having a damping optimum at $m^* \approx 2.50$ . Moreover, a novel digital object tracking (DOT) method using vorticity-magnitude iso-surfaces is implemented to analyse vortical structures. A similar vortex shedding topology is observed for various mass ratios $m^*$ . Our observations show that first, a vortex ring in the pendulum's wake is formed. Soon after, the initial ring breaks down to two clearly distinguishable structures of similar size. One of the two vortices remains on the circular path of the pendulum, while the other detaches, propagates downwards, and eventually dissipates. The time when the first vortex is shed, and its initial propagation velocity, depend on $m^*$ and the momentum imparted by the spherical bob. The findings further show good agreement between the experimentally determined vortex shedding frequency and the theoretical vortex shedding time scale based on the Strouhal number.

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The spatio-temporal distribution of residence times and water ages in groyne fields plays an important role for a number of biotic processes, particularly conditioning nutrient dynamics and phytoplankton growth. Experimental determination of these parameters involves time-consuming field work and is often limited to the water surface depending on the methodology applied. Computational fluid dynamics (CFD) can be used as efficient tool for direct modelling of residence times, limiting additional field work to collect data necessary for model calibration and validation. The objective of this study is to derive, test and apply a numerical particle-tracing method to model these flow characteristics based on the output of a three-dimensional hydrodynamic model for turbulent river flow. This allows for an evaluation of residence times and water ages at an arbitrary elevation within the water column. Virtual particles are released in a control volume, and their paths and travel times to and from the main stream are traced using a random-walk approach based on the spatial distribution of turbulent kinetic energy to account for turbulent fluctuations. The modelling approach was successfully validated for the water surface using field data measured in a groyne field of the Danube River in Austria. Particle-tracing experiments were carried out for several discharges to study the evolution of residence times and water ages with varying runoff. It was found that discharges at which overtopping of the groynes begins lead to significantly higher residence times and water ages than runoff higher or lower than this characteristic value. These findings are expected to be transferable for groyne fields of similar geometry and crest height.