This study examines whether the dispersion of passive particles at the free surface of a generic (nonturbulent) shallow flow can reliably represent the behavior of depth-keeping particles below the surface. A shallow configuration characterize many aquatic environments, such as coastal regions and lakes, where horizontal scales far exceed vertical ones, large-scale flow structures dominate, and observations are sometimes limited to the surface. We compare surface and subsurface horizontal velocities in both direction and magnitude, identifying distinct behaviors depending on the parameter $Re_Fδ^2$, where $Re_F$ is the Reynolds number based on forcing, and $δ$ is the aspect ratio between the fluid layer depth and the horizontal forcing scale. At low $Re_Fδ^2$, deep flows match the surface flow in direction throughout the layer, but not in magnitude. At high $Re_Fδ^2$, the magnitude matches (outside the bottom boundary layer), but not always the direction. Despite these differences, for all $Re_Fδ^2$, surface particle patterns correlate with those in the upper quarter of the fluid layer. Filamentary structures caused by horizontal flow convergence remain spatially aligned within this region. Below it, at intermediate $Re_Fδ^2$, deep filaments become diffuse and eventually vanish. At high $Re_Fδ^2$, filaments persist at depth, but become spatially misaligned with surface filaments. These findings suggest that in shallow environments, surface observations can quantitatively infer subsurface transport processes in the upper quarter of the fluid layer. For the deeper part, knowledge of the vertical profiles of the mean flow yields insights into the horizontal transport processes.
Nonlinear theory of magnetohydrodynamic flows of stratified rotating plasma in two-layer shallow water approximation. Rossby waves and their three-wave interactions
