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.

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.

Lateral flow significantly contributes to the near-bottom mass transport of salinity in a channel-shoal system. In this study, an integrated tripod system was deployed in the transition zone of a channel-shoal system of the Changjiang Estuary (CE), China, to observe the near-bottom physics with high temporal/spatial resolution, particularly focusing on the lateral-flow-induced mass transport. These in situ observations revealed a small-scale salinity fluctuation around low water slack during moderate and spring tidal conditions. A simultaneous strong lateral current was also observed, which was responsible for this small-scale fluctuation. A high-resolution unstructured-grid Finite-Volume Community Ocean Model has been applied for the CE to better understand the mechanism of this lateral flow and its impact on salinity transport. The model results indicate that a significant southward near-bed shoal-to-channel current is generated by the salinity-driven baroclinic pressure gradient. This lateral current affects the salinity transport pattern and the residual current in the cross-channel direction. Cross-channel residual current shows a two-layer structure in the vertical, especially in the intermediate tide when the lateral flow notably occurred. Both observation and model results indicate that near-bottom residual transport of water moved consistently southward (shoal to channel). Mechanisms for this intratidal salinity variation and its implications can be extended to other estuaries with similar channel-shoal features.