Abstract
In this paper, a three-dimensional semi-idealized model for tidal motion in a tidal estuary of arbitrary shape and bathymetry is presented. This model aims at bridging the gap between idealized and complex models. The vertical profiles of the velocities are obtained analytically in terms of the first-order and the second-order partial derivatives of surface elevation, which itself follows from an elliptic partial differential equation. The surface elevation is computed numerically using the finite element method and its partial derivatives are obtained using various methods. The newly developed semi-idealized model allows for a systematic investigation of the influence of geometry and bathymetry on the tidal motion which was not possible in previously developed idealized models. The new model also retains the flexibility and computational efficiency of previous idealized models, essential for sensitivity analysis. As a first step, the accuracy of the semi-idealized model is investigated. To this end, an extensive comparison is made between the model results of the semi-idealized model and two other idealized models: a width-averaged model and a three-dimensional idealized model. Finally, the semi-idealized model is used to understand the influence of local geometrical effects on the tidal motion in the Ems estuary. The model shows that local convergence and meandering effects can have a significant influence on the tidal motion. Finally, the model is applied to the Ems estuary. The model results agree well with observations and results from a complex numerical model.
Highlights
Estuaries are regions of large economical and ecological importance
It is important to mention that for quadratic basis functions, the unreliable behavior of the ZZ-method for computing the first-order and the second-order partial derivatives with sufficiently large number of nodes is independent of the choice of the bed profile
The surface elevation itself follows from a two-dimensional linear elliptic partial differential equation which is solved numerically using the finite element method
Summary
Estuaries are regions of large economical (navigation channels, sand and gas mining, recreation, etc.) and ecological importance. Winant (2007) developed a three-dimensional idealized model for tidal motion on a rotating (Coriolis effects included) elongated (width is much smaller than the length) rectangular domain with a parabolic bathymetric profile in the lateral direction together with constant physical parameters and constant density. The vertical profile of the three-dimensional velocity can be explicitly calculated in terms of the first and second-order partial derivatives of the surface elevation, i.e., the three-dimensional velocity profile is analytic in the vertical direction This model is a first step in bridging the gap between idealized models and complex models: the model can still be systematically analyzed to gain understanding of important physical mechanisms, but allows for more complex geometries and bathymetries.
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