*5.1. Calculation of Hydrodynamics in Estuaries*

The estuary is a transitional region which connects the inland rivers and coastal regions, and is still often regarded as a shallow water system. In existing studies, the nonhydrostatic models and the SWE models are both widely used to simulate estuarine flows.

Relative to SWE models, 3D nonhydrostatic models can include influences of nonhydrostatic pressures which are significant when the ratio of the vertical scale to horizontal scale of motions of flows is not small. Examples are flows over abruptly changing bed topographies, flows with sharp density gradients, and short-wave motions (e.g., waves in coastal and ocean regions). In these cases, the hydrostatic assumption is no longer valid. A short review of certain kinds of 3D nonhydrostatic models can be found in the authors' former studies [9]. Generally, for shallow water systems such as estuary regions, the results simulated by an SWE model are quite similar to those by a 3D nonhydrostatic model. Moreover, a 3D nonhydrostatic model (e.g., 10 layers are used in vertical direction) is at least tens of times slower than a 2D SWE model. It may take more than a month to complete a high-resolution simulation of the 2011–2013 process of the flow, sediment transport, and riverbed evolution in the Yangtze Estuary using the current computing technology used in this paper. Without resorting to simplified methods (e.g., local models, morphological scale factors), high-resolution simulations of long-term processes of flow and sediment transport in the entire Yangtze Estuary using a 3D nonhydrostatic model have not ye<sup>t</sup> been reported.

The SWE models, applied to simulations of estuarine flows, include the 2D SWE models [8,10,13, 18,19,39–41] and the 3D SWE model (e.g., [12,23,24,42–45]). The two kinds of SWE models both use the hydrostatic assumption. On the one hand, high-resolution simulations of short-term processes of tides (e.g., [39,41]), salinity transport (e.g., [8,40–44]), pollutant transport (e.g., [45]) and sediment concentration fields at selected times (e.g., [46]) in the Yangtze Estuary have been gradually enabled due to continuous improvements in computers in the past two decades. On the other hand, the huge computation cost, brought about by simulations of long-term fluvial processes in the Yangtze Estuary using high-resolution grids and small time steps, still challenges most existing 2D/3D numerical codes. In real applications, most of the simulations of hydrodynamics of the Yangtze Estuary take two steps. First, the seaward open boundaries are forced by the time series of tidal levels which are predicted by a GTM such as in [29]. Second, the hydrodynamics of the estuary are simulated by 2D or 3D SWE models. As a result, simulations of the ocean waves, which may be characterized by strong nonhydrostatic pressures and beyond the estuary regions, are in essence not needed. Hence, the application of time-consuming nonhydrostatic 3D models can be totally avoided.

Following the existing studies using SWE models, we adopted a 2D SWE model to perform the simulation of the flow and sediment transport in the Yangtze Estuary in this paper.
