Physics-informed neural networks (PINNs) are increasingly being used in various scientific disciplines. However, dealing with non-stationary physical processes remains a significant challenge in such models, whereas fluid motions are typically non-stationary. In this study, a PINN-based method was designed and optimized to solve non-stationary fluid dynamics with shallow water equations in a polar coordinate system (PINN-SWEP). It was developed and validated with a classic circular basin case that is well-documented in scientific literature. In the validation case, the wind-induced water surface fluctuations are less than 1 cm, posing challenges in modeling. However, our PINN-SWEP model can accurately simulate such tiny water surface fluctuations and resolve complex fluid motions based on limited and sparse data. A boundary discontinuity problem associated with the use of a polar coordinate system is further discussed and improved, thereby enhancing the applicability of PINN in water research. The methodology can provide an alternative solution for numerical or analytical solutions with high accuracy.

Accurate and efficient prediction of spatiotemporal variations in the distribution of substances in fluids (SIFs) is crucial for various aspects of fluid mechanics related research and applications, involving for instance, material transport quantification, water quality assessment, and engineering condition analysis. This study proposes a framework for resolving the spatiotemporal distribution of SIFs such as salt and suspended sediment based on water levels and flow velocities. The framework incorporates a deep learning model based on a classic neural operator (DeepONet) architecture, which consists of a feature network and a position network to encode the characteristics of input variables and the problem domain. Numerical simulations were performed to generate the needed datasets. The framework was well-validated by predicting salinity and suspended sediment concentration (SSC) distributions in two idealized cases and a real-word case, demonstrating its efficacy and robustness. Time-series validation further demonstrated the prediction accuracy of the framework. The deep learning model is also capable of enhanced-resolution predictions, enabling the generation of high-resolution spatial distributions of SIFs from low-resolution hydrodynamic data. Both bottom and surface layers of the water column were analyzed, revealing that the mapping relationships between hydrodynamics and SIF distributions can be accurately captured throughout the water column, despite variations in correlation coefficients. Due to these capabilities and advantages, additional data sources can be integrated into the framework in the future, highlighting its considerable potential for broader applications in aquatic environments.

Existing knowledge about groyne-induced effects is primarily based on riverine or coastal environments where salinity gradients are absent or limited. However, in estuaries, salinity gradients drive physical processes such as longitudinal and lateral residual flows. The effect of groynes is much more complex because they can modulate channel hydrodynamics and directly affect lateral salinity gradients. In this study, an idealized model is applied to investigate the effects of groyne layouts in estuarine environments, including effects on (1) channel hydrodynamics, (2) lateral water exchange, (3) Coriolis effects, and (4) saltwater intrusion. Model results show that the aspect ratio (the width of groyne fields to the length of groynes) of groyne fields plays an important role. Groynes also induce asymmetry of lateral flows, for example, increasing near-bottom shoal-to-channel flows during low water slack. The aspect ratio has opposite effects on horizontal and vertical components of water exchange. A large aspect ratio strengthens horizontal exchange and weakens density-driven currents. For a large-scale groyne field (several kilometers), Coriolis effects introduce a substantial difference in exchange mechanisms along the north and south banks. A medium range of aspect ratio (2.0-3.0) leads to the strongest saltwater intrusion during both neap and spring tides.

Lateral flows redistribute sediment and influence the morphodynamics of channel-shoal systems. However, our understanding of lateral transport of suspended sediment during high and low water slack is still fairly limited, especially in engineered estuaries. Human interventions such as dike-groyne structures influence lateral exchange mechanisms. The present study aims to unravel these mechanisms in a heavily engineered, turbid channel-shoal system in the Changjiang Estuary, using a high-resolution unstructured-grid three-dimensional model and in situ observations. Analysis of model results reveals two typical transport patterns during slack-water conditions, that is, shoal-to-channel transport during low water slack and channel-to-shoal transport during high water slack. A momentum balance analysis is carried out to explain mechanisms driving the lateral transport of suspended sediment during high water slack, revealing the importance of lateral pressure gradients, Coriolis force, and the curvature-induced term. Groyne fields play a crucial role in sediment transport, especially during low water slack. A model scenario in which one groyne is removed reveals that groyne fields strongly influence lateral sediment transport. The decomposition of the sediment transport flux reveals that the turbidity maximum is shaped by a balance between seaward advection by residual flows, and landward transport by tidal pumping and gravitational circulation. Within the turbidity maximum, sediment is laterally redistributed by lateral flows during slack-water conditions, greatly influencing estuarine channel morphology.