A finite volume model for two-layer shallow water flow in microtidal salt-wedge estuaries is presented in this work. The governing equations are a coupled system of shallow water equations with source terms accounting for irregular channel geometry and shear stress at the bed and interface between the layers. To solve this system we applied the Q-scheme of Roe with suitable treatment of source terms, coupling terms, and wet-dry fronts. The proposed numerical model is explicit in time, shock-capturing and it satisfies the extended conservation property for water at rest. The model was validated by comparing the steady-state solutions against a known arrested salt-wedge model and by comparing both steady-state and time-dependant solutions against field observations in Rječina Estuary in Croatia. When the interfacial friction factor λi was chosen correctly, the agreement between numerical results and field observations was satisfactory.
Arita, M., Jirka, G.H., 1987. Two-layer model of saline wedge. II: Prediction. J. Hydraul. Eng., 113, 10, 1249-1263.
Armi, L., 1986. The hydraulics of two flowing layers with different densities. J. Fluid Mech., 163, 27-58.
Balloffet, A., Borah, D.K., 1985. Lower Mississippi Salinity Analysis. J. Hydraul. Eng., 111, 2, 300-315.
Bermudez, A., Vázquez-Cendón, M., 1994. Upwind methods for hyperbolic conservation laws with source terms. Comput. Fluids, 23, 8, 1049-1071.
Brufau, P., 2002. A numerical model for the flooding and drying of irregular domains. Int. J. Numer. Methods Fluids, 39, 3, 247-275.
Castro, M.J., Macias, J., Parés, C., 2001. A Q-scheme for a class of systems of coupled conservation laws with source term. Application to a two-layer 1D shallow water system. ESAIM Math. Model. Numer. Anal., 35, 1, 107-127.
Castro, M.J., Garcia-Rodriguez, J., González-Vida, J.M., Macas, J., Parés, C., Vázquez-Cendón, M., 2004. Numerical simulation of two-layer shallow water flows through channels with irregular geometry. J. Comput. Phys., 195, 1, 202-235.
Castro, M.J., Ferreiro Ferreiro, A., García-Rodríguez, J., González- Vida, J., Macas, J., Parés, C., Elena Vázquez-Cendón, M., 2005. The numerical treatment of wet/dry fronts in shallow flows: application to one-layer and two-layer systems. Math. Comput. Model., 42, 3-4, 419-439.
Castro, M.J., Gonzales-Vida, J., Pares, C., 2006. Numerical treatment of wet/dry fronts in shallow flows with a modified Roe scheme. Math. Models Methods Appl. Sci., 16, 6, 897-934.
Castro, M.J., García-Rodríguez, J.A., González-Vida, J.M., Macas, J., Parés, C., 2007. Improved FVM for two-layer shallow-water models: Application to the Strait of Gibraltar. Adv. Eng. Softw., 38, 6, 386-398.
Castro, M.J., Dumbser, M., Pares, C., Toro, E.F., 2009a. ADER schemes on unstructured meshes for nonconservative hyperbolic systems: applications to geophysical flows. Comp. & Fluids, 38, 1731-1748.
Castro, M.J., Fernández-Nieto, E.D., Ferreiro, A.M., García- Rodríguez, J.A., Parés, C., 2009b. High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems. Journal of Scientific Computing, 39, 1, 67-114.
Castro, M.J., Fernandez-Nieto, E.D., Gonzalez-Vida, J.M., Pares, C., 2011. Numerical treatment of the loss of hyperbolicity of the two-layer shallow-water system. J. Sci. Comput., 48, 1, 16-40.
Dazzi, R., Tomasino, M., 1974. Mathematical model of salinity intrusion in the delta of the Po River. Coast. Eng. Proc., 134, 2302-2321.
Dermissis, V., Partheniades, E., 1985. Dominant shear stresses in arrested saline wedges. J. Waterw. Port, Coastal, Ocean Eng., 111, 4, 733-752.
Farmer, D., Armi, L., 1986. Maximal two-layer exchange over a sill and through the combination of a sill and contraction with barotropic flow. J. Fluid Mech., 164, 53-76.
Geyer, W.R., Ralston, D.K., 2011. The dynamics of strongly stratified estuaries. In: Wolanski, E., McLusky, D. (Eds.): Treatise on Estuarine and Coastal Science, Volume 2, Elsevier, pp. 37-52.
Grubert, J., 1989. Interfacial mixing in stratified channel flows. J. Hydraul. Eng., 115, 7, 887-905.
Hansen, D., Rattray Jr, M., 1966. New dimensions in estuary classification. Limnol. Oceanogr., 11, 3, 319-326.
Harten, A., 1984. On a class of high resolution total-variationstable finite-difference schemes. SIAM J. Numer. Anal., 21, 1, 1-23.
Johnson, B., Boyd, M., Keulegan, G., 1987. A Mathematical Study of the Impact on Salinity Intrusion of Deepening the Lower Mississippi River Navigation Channel. Technical Report April, US Army Corps of Engineers, Vicksburg, Mississippi.
Krvavica, N., Mofardin, B., Ruzic, I., Ozanic, N., 2012. Measurement and analysis of salinization at the Rječina estuary. Gradevinar, 64, 11, 923-933.
Liu, H., Yoshikawa, N., Miyazu, S., Watanabe, K., 2015. Influence of saltwater wedges on irrigation water near a river estuary. Paddy Water Environ., 13, 2, 179-189.
Ljubenkov, I., 2015. Hydrodynamic modeling of stratified estuary: case study of the Jadro River (Croatia). J. Hydrol. Hydromech., 63, 1, 29-37.
Rebollo, T.C., Dom, A., Fern, E.D., 2003. A family of stable numerical solvers for the shallow water equations with source terms. Comput. Methods Appl. Mech. Eng., 192, 1-2, 203-225.
Roe, P., 1981. Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comput. Phys., 43, 2, 357-372.
Sargent, F.E., Jirka, G.H., 1987. Experiments on saline wedge. J. Hydraul. Eng., 113, 10, 1307-1323.
Schijf, J., Schönfeld, J., 1953. Theoretical considerations on the motion of salt and fresh water. In: Proc. Minnesota Int. Hydraul. Conv., ASCE, Minneapolis, Minnesota, pp. 321-333.
Sierra, J.P., Sánchez-Arcilla, a., Figueras, P. a., González del Ro, J., Rassmussen, E.K., Mösso, C., 2004. Effects of discharge reductions on salt wedge dynamics of the Ebro River. River Res. Appl., 20, 1, 61-77.
Stommel, H.M., Farmer, H.G., 1952. On the nature of estuarine circulation, part 1, chap. 3 and 4. Technical report. Woods Hole Oceanographic Institution, Woods Hole, Massachusetts.
Vázquez-Cendón, M.E., 1999. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J. Comput. Phys., 148, 2, 497-526.