{"refrec":{"BRefID":368855,"RR":"<b>Rozendaal, M.P.; Dijkstra, Y.M.; Schuttelaars, H.M.</b> (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.","BEntID":366581,"PublicFlag":1,"CheckedFlag":0,"wosflag":0,"vabbflag":0,"RefStringPartII":". TU Delft/Waterbouwkundig Laboratorium: Delft; Antwerp.  67 pp.","DocTypID":13,"DocType":"Reports","MarineFlag":0,"FreshFlag":0,"BrackishFlag":0,"TerrestrialFlag":0,"Authorstring":"Rozendaal, M.P.; Dijkstra, Y.M.; Schuttelaars, H.M.","OrigTitleTranslFlag":0,"Authorstringtrunc":"Rozendaal, M.P.; Dijkstra, Y.M.; Schuttelaars, H.M.","Englishabstract":"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. 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