A three–dimensional model for water motion in a tidally dominated estuary: Overtides and Residual flow
Rozendaal, M.P.; Dijkstra, Y.M.; Schuttelaars, H.M. (2022). A three–dimensional model for water motion in a tidally dominated estuary: Overtides and Residual flow. TU Delft/Waterbouwkundig Laboratorium: Delft; Antwerp. 67 pp.
In this document, the hydrodynamic equations are derived that govern the tidal dynamics in estuaries and coastal seas. The three-dimensional shallow water equations are reduced in complexity by using a scaling analysis, perturbation method and harmonic decomposition. The derivation starts from the three-dimensional shallow water equations. Using a scaling analysis, a small parameter is identified which is then used to determine the order of magnitude of each term. A perturbation method is used to establish which terms balance at leading, first and higher order. All non-linear terms are of first and higher order. The leading-order balances are therefore linear and much easier to solve then the original non-linear equations. The non-linear and higher-order terms are not neglected, but are instead included in the higher-order balances. The non-linearities act as forcing mechanisms in the linear higher-order balances. The linearity of the balances at each order allows the effect of individual forcing mechanisms to be identified. The time dependency of the water motion is resolved using harmonic decomposition.
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