Sea waves transport of inertial micro-plastics: Mathematical model and applications

Plastic pollution in seas and oceans has recently been recognized as one of the most impacting threats for the environment, and the increasing number of scientific studies proves that this is an issue of primary concern. Being able to predict plastic paths and concentrations within the sea is therefore fundamental to properly face this challenge. In the present work, we evaluated the effects of sea waves on inertial micro-plastics dynamics. We hypothesized a stationary input number of particles in a given control volume below the sea surface, solving their trajectories and distributions under a second-order regular wave. We developed an exhaustive group of datasets, spanning the most plausible values for particles densities and diameters and wave characteristics, with a specific focus on the Mediterranean Sea. Results show how the particles inertia significantly affects the total transport of such debris by waves

Influence of initial conditions on absolute and relative dispersion in semi-enclosed basins

Absolute and relative dispersion are fundamental quantities employed in order to assess the mixing strength of a basin. There exists a time scale called Lagrangian Integral Scale associated to absolute dispersion that highlights the occurrence of the transition from a quadratic dependence on time to a linear dependence on time. Such a time scale is commonly adopted as an indicator of the duration needed to lose the influence of the initial conditions. This work aims to show that in a semi-enclosed basin the choice of the formulation in order to calculate the absolute dispersion can lead to different results. Moreover, the influence of initial conditions can persist beyond the Lagrangian Integral Scale. Such an influence can be appreciated by evaluating absolute and relative dispersion recursively by changing the initial conditions. Furthermore, finite-size Lyapunov exponents characterize the different regimes of the basin

Turbulence in Rivers

The study of turbulence has always been a challenge for scientists working on geophysical flows. Turbulent flows are common in nature and have an important role in geophysical disciplines such as river morphology, landscape modeling, atmospheric dynamics and ocean currents. At present, new measurement and observation techniques suitable for fieldwork can be combined with laboratory and theoretical work to advance the understanding of river processes. Nevertheless, despite more than a century of attempts to correctly formalize turbulent flows, much still remains to be done by researchers and engineers working in hydraulics and fluid mechanics. In this contribution we introduce a general framework for the analysis of river turbulence. We revisit some findings and theoretical frameworks and provide a critical analysis of where the study of turbulence is important and how to include detailed information of this in the analysis of fluvial processes. We also provide a perspective of some general aspects that are essential for researchers/ practitioners addressing the subject for the first time. Furthermore, we show some results of interest to scientists and engineers working on river flows

Detection of Lagrangian Coherent Structures due to shallow water macrovortices in compound channels

Water quality management is a crucial aspect for a riverine environment, since it hosts a great variety of wildlife that can be dramatically influenced by the controlled and uncontrolled release of pollutants in the rivers themselves. All strategies to monitor the water quality must take into account the complex processes involved in the mass transport related to the river flows. These processes should be studied in a Lagrangian framework more than from an Eulerian point of view. Several techniques are now available to describe and quantify the relevant characteristics of the mixing processes, i.e. Lagrangian statistics in terms of single and multiple particles dynamics. However, applying the standard Taylor theory of the dispersion, which leads to the evaluation of the averaged dispersion coefficients, has some intrinsic limitations that are related to the average over a great number of trajectories in the entire domain under investigation. In the present study, we apply the techniques that derive from the nonlinear dynamical system theory to a riverine situation, in which the natural shape of the river cross-section is accounted for. These techniques allow for the detection of the so-called Lagrangian Coherent Structures (LCS), which are material elements embedded in the flow that strongly influence the mixing processes. Indeed LCSs represents material barriers that can separate the domain in distinct regions with no mass transport among them. We investigate the possibility of formation of LCSs in a compound channel under uniform flow conditions depending on the main physical parameters

Eulerian spectrum of finite-time Lyapunov exponents in compound channels

Fluid flows reveal a wealth of structures, such as vortices and barriers to transport. Usually, either an Eulerian or a Lagrangian frame of reference is employed in order to detect such features of the flow. However, the two frameworks detect structures that have different properties. Indeed, common Eulerian diagnostics (Hua-Klein and Okubo-Weiss criterion) employed in order to detect vortices do not always agree with Lagrangian diagnostics such as finite-time Lyapunov exponents. Besides, the former are Galilean-invariant whereas the latter is objective. However, both the Lagrangian and the Eulerian approaches to coherent structure detection must show some links under any inertial-frame. Compound channels flows have been accurately studied in the past, both from a Lagrangian and an Eulerian point of view. The features detected do not superimpose: Eulerian vortices do not coincide with barriers to transport. The missing link between the two approaches is here recovered thanks to a spectral analysis

Turbulent characteristics and Lagrangian Coherent Structures (LCS) in uniform compound channels

A great variety of natural water streams and artificial channels can be classified as \u201cshallow compound channels\u201d since their cross-stream section can be assumed to be characterized by a main central channel and shallow floodplains with a marked separation in the typical length scales involved, since their horizontal dimensions exceed the vertical dimension, see Jirka & Uijttewaal (2004). In the case of shallow free surface flows, two-dimensional coherent structures with length scales greater than the water depth are often observed in a wide range applications, Socolofsky & Jirka (2004). The typical geometry of the compound channels are such that the topography has a sharp discontinuity in the boundary between the main channel and the flood plains. As a result, the flow velocity in the floodplains is lower than in the main channel, due to the water shallowness and to the high bed roughness (e.g. presence of vegetation). The consequent shearing is a source of vorticity that is transported along the longitudinal direction. Moreover, the flow depth gradient along the cross section is indeed another fundamental source of vorticity that produces large scale vertical structures, as shown in (Soldini et al, 2004). Such turbulent structures are liable of the transfer of momentum and mass between the central main channel and floodplains. The present study is focused on the description of the dynamics undergone by macrovortices in a compound channel under statistically steady condition of flow. We show experimentally how the large scale vortical structures, after an initial grows starting from the inlet, reach a constant typical dimensions that remains unchanged along the streamwise direction. The typical vortex dimensions scale with the flow depth jump between the main channel and the floodplains. Further, the mixing processes associated to the above turbulent structures are analyzed in details with the aid of different mixing measures, such as the Hua and Klein criterion (Hua & Kein, 1998), the Finite Time Lyapunov Exponents (FTLE) and the absolute and relative statistics. If, on one hand, the mean particle statistics are able to discriminate the overall mixing regime, according to the classical Taylor theory, on the other hand, different measures as the FTLE are able to identify Lagrangian Coherent Structures (LCS) inside the Eulerian flow fields, enlightening the presence of transport barriers (Boffetta et al. 2001) that may prevent the exchange of mass between the main channel and the flood plains