Lagrangian dispersion in shallow flows

Flows in marine and freshwater environments continuously transport materials from one place to another, with a probability to deposit them along the way. This advective and dispersive process is complex due to the variety of transported material, which includes plastics, sediments, microorganisms, as well as the wide range of spatial and temporal scales of the carrier flow. Typically, these environments are shallow. Shallowness imparts distinctive characteristics to the flows because of vertical confinement. Shallow flows are characterized by the presence of large-scale horizontal (primary) vortices and weaker, yet still significant, secondary flows with both horizontal and vertical velocity components. These secondary motions create a three-dimensional (3D) flow structure that is often overlooked, as shallow flows are commonly assumed to be two-dimensional, particularly in studies of particle transport, which have traditionally focused on horizontal dispersion driven by the primary vortices. It is this 3D structure that leads to vertical dispersion and to the vertical variation of horizontal dispersion, both of which have not been fully explored. The aim of this thesis is to investigate these 3D aspects of particle dispersion in shallow flows. For this purpose, 3D numerical simulations are employed to generate a generic shallow flow by continuously forcing a thin layer of fluid that is vertically confined by a stress-free top and a no-slip bottom boundary. First, the characteristics of the resulting forced shallow flows are described and explained by performing a parameter study varying the fluid layer depth and the Reynolds number based on the forcing. The flows display, in general, an asymmetric distribution of vertical velocities: broad, weak upwellings surrounded by narrow, strong downwellings. These vertical flows are linked to horizontal flow structures, with updrafts occurring in vorticity-dominated regions and downdrafts in strain-dominated regions. With this information, we examine the vertical dispersion of passive particles. When there is significant asymmetry in the vertical velocities, particles in updrafts ascend slowly, while particles in downdrafts descend rapidly. The particles remain trapped longer in updrafts than in downdrafts due to their association with vorticity-dominated areas. Next, vertical dispersion is explored further for particles that actively swim towards a target depth within the shallow layer. When such particles swim towards a depth near the surface, they tend to accumulate in downdrafts, while those aiming for a depth near the bottom concentrate in updrafts. In steady flows, this behavior does not significantly alter the vertical distribution of particles. However, in unsteady flows, distinct vertical distributions emerge due to the correlation between updrafts and vortices, and between downdrafts and strain-dominated regions. Finally, the distributions of passive particles at the surface are compared with those of depth-keeping particles at various depths to assess whether surface patterns reflect subsurface features. Surface particles form filamentous structures, which also appear at depth due to the depth-keeping nature of the particles. Regardless of flow conditions, subsurface filaments closely match those at the surface within the upper quarter of the layer. Below this region, the similarities between filaments weakens depending on the flow conditions, either due to the breakdown of deeper filaments or spatial misalignment between surface and deep filaments. At greater depths, within the viscous boundary layer, particles form point-like clusters that are completely decoupled from surface patterns. Overall, this dissertation demonstrates that shallow flows exhibit asymmetries in both vertical velocities and their associated horizontal structures, which strongly affect the vertical spreading of passive particles and the vertical distribution of swimming particles. Moreover, the vertical flow structure causes horizontal dispersion of passive particles to vary significantly with depth, limiting our ability to infer deeper dispersion based on surface observations. These findings emphasize that neglecting vertical motions or relying solely on surface observations risks overlooking key features of transport in shallow flows.