Periodic water waves generate Stokes drift as manifest from the orbits of Lagrangian particles not fully closing. Stokes drift can contribute to the transport of floating marine litter, including plastic. Previously, marine litter objects have been considered to be perfect Lagrangian tracers, travelling with the Stokes drift of the waves. However, floating marine litter objects have large ranges of sizes and densities, which potentially result in different rates of transport by waves due to the non-Lagrangian behaviour of the objects. Through a combination of theory and experiments for idealised spherical objects in deep-water waves, we show that different objects are transported at different rates depending on their size and density, and that larger buoyant objects can have increased drift compared with Lagrangian tracers. We show that the mechanism for the increased drift observed in our experiments comprises the variable submergence and the corresponding dynamic buoyancy force components in a direction perpendicular to the local water surface. This leads to an amplification of the drift of these objects compared to the Stokes drift when averaged over the wave cycle. Using an expansion in wave steepness, we derive a closed-form approximation for this increased drift, which can be included in ocean-scale models of marine litter transport.

The net movement of Lagrangian particles under water waves comprises a Stokes drift in the direction of wave propagation and an Eulerian return flow in the opposing direction. Accurate prediction of the Eulerian return flow in the ocean is of importance in modeling the transport of plastic pollution, oil, wreckage, and sediment. Herein, we derive a multiple-scales solution for the Eulerian mean flow under wave packets that is valid for all water depths, relative to both the length of the wave and the length of the wave packet. To validate this solution, we carry out particle tracking velocimetry experiments in a long flume to extract the mean motion from Lagrangian seeding particles under wave packets, finding good agreement. The extraction technique is able to deal with small background motion and subharmonic error waves associated with wave generation by the paddle, the latter being relatively large in finite-depth flume experiments. In finite depth, the return flow is forced by both the divergence of the Stokes transport on the wave-packet scale and the formation of a non-negligible mean set-down underneath the packet, which acts like a bounding streamtube in the form of a convergent-divergent duct. The magnitude of the horizontal return flow is thus enhanced, with particular relevance to transport in the finite-depth coastal environment.

The development and application of numerical models to investigate fluvial sedimentary archives has increased during the last decades resulting in a sustained growth in the number of scientific publications with keywords, 'fluvial models', 'fluvial process models' and 'fluvial numerical models'. In this context we compile and review the current contributions of numerical modelling to the understanding of fluvial archives. In particular, recent advances, current limitations, previous unexpected results and future perspectives are all discussed. Numerical modelling efforts have demonstrated that fluvial systems can display non-linear behaviour with often unexpected dynamics causing significant delay, amplification, attenuation or blurring of externally controlled signals in their simulated record. Numerical simulations have also demonstrated that fluvial records can be generated by intrinsic dynamics without any change in external controls. Many other model applications demonstrate that fluvial archives, specifically of large fluvial systems, can be convincingly simulated as a function of the interplay of (palaeo) landscape properties and extrinsic climate, base level and crustal controls. All discussed models can, after some calibration, produce believable matches with real world systems suggesting that equifinality - where a given end state can be reached through many different pathways starting from different initial conditions and physical assumptions - plays an important role in fluvial records and their modelling. The overall future challenge lies in the development of new methodologies for a more independent validation of system dynamics and research strategies that allow the separation of intrinsic and extrinsic record signals using combined fieldwork and modelling.