General shallow water equations (GSWEs)

References

• Adduce, C., Sciortino, G., & Proietti, S. (2012). Gravity currents produced by lock exchanges: Experiments and simulations with a two-layer shallow-water model with entrainment. Journal of Hydraulic Engineering, 138(2), 111–121. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000484
   Web of Science ®Google Scholar
• Ayog, J. L., Kesserwani, G., Shaw, J., Sharifian, M. K., & Bau, D. (2021). Second-order discontinuous Galerkin flood model: Comparison with industry-standard finite volume models. Journal of Hydrology, 594, Article 125924. https://doi.org/10.1016/j.jhydrol.2020.125924
   Google Scholar
• Bear, J. (1972). Dynamics of fluids in porous media. Elsevier.
   Google Scholar
• Carraroa, F., Valiania, A., & Calef, V. (2018). Efficient analytical implementation of the DOT Riemann solver for the de Saint Venant-Exner morphodynamic model. Advances in Water Resources, 113, 189–201. https://doi.org/10.1016/j.advwatres.2018.01.011
   Web of Science ®Google Scholar
• Dong, B., Xia, J., Zhou, M., Deng, S., Ahmadian, R., & Falconer, R. A. (2021). Experimental and numerical model studies on flash flood inundation processes over a typical urban street. Advances in Water Resources, 147, Article 103824. https://doi.org/10.1016/j.advwatres.2020.103824
   Google Scholar
• Finnigan, J. J. (2000). Turbulence in plant canopies. Annual Review of Fluid Mechanics, 32(1), 519–571. https://doi.org/10.1146/fluid.2000.32.issue-1
   Web of Science ®Google Scholar
• Hibberd, S., & Peregrine, D. H. (1979). Surf and run-up on a beach: A uniform bore. Journal of Fluid Mechanics, 95(2), 323–345. https://doi.org/10.1017/S002211207900149X
   Web of Science ®Google Scholar
• Hubbard, M. E., & Dodd, N. (2000). A 2D numerical model of wave run-up and overtopping. Coastal Engineering, 47, 1–26. https://doi.org/10.1016/S0378-3839(02)00094-7
   Web of Science ®Google Scholar
• Lahaye, N., & Zeitlin, V. (2022). Coherent magnetic modon solutions in quasi-geostrophic shallow water magnetohydrodynamics. Journal of Fluid Mechanics, 941, Article A15. https://doi.org/10.1017/jfm.2022.289
   Google Scholar
• Li, Q., Liang, Q., & Xia, X. (2020). A novel 1D-2D coupled model for hydrodynamic simulation of flows in drainage networks. Advances in Water Resources, 137, Article 103519. https://doi.org/10.1016/j.advwatres.2020.103519
   Google Scholar
• Mignot, E., Paquier, A., & Haider, S. (2006). Modeling floods in a dense urban area using 2D shallow water equations. Journal of Hydrology, 327(1–2), 186–199. https://doi.org/10.1016/j.jhydrol.2005.11.026
   Web of Science ®Google Scholar
• Neal, J., Villanueva, I., Wright, N., Willis, T., Fewtrell, T., & Bates, P. (2012). How much physical complexity is needed to model flood inundation? Hydrological Processes, 26(15), 2264–2282. https://doi.org/10.1002/hyp.v26.15
   Web of Science ®Google Scholar
• Nikora, V., Ballio, F., Coleman, S., & Pokrajac, D. (2013). Spatially-averaged flows over mobile rough beds: Definitions, averaging theorems, and conservation equations. Journal of Hydraulic Engineering, 139(8), 803–811. https://doi.org/10.1061/(ASCE)HY.1943-7900.0000738
   Web of Science ®Google Scholar
• Nikora, V. I., Goring, D. G., McEwan, I., & Griffiths, G. (2001). Spatially-averaged open-channel flow over a rough bed. Journal of Hydraulic Engineering, 127(2), 123–133. https://doi.org/10.1061/(ASCE)0733-9429(2001)127:2(123)
   Web of Science ®Google Scholar
• Papadopoulos, K., Nikora, V., Cameron, S., Stewart, M., & Gibbins, C. (2020). Spatially-averaged flows over mobile rough beds: Equations for the second-order velocity moments. Journal of Hydraulic Research, 58(1), 133–151. https://doi.org/10.1080/00221686.2018.1555559
   Web of Science ®Google Scholar
• Pedras, M. H. J., & M. J. S. de Lemos (2000). On the definition of turbulent kinetic energy for flow in porous media. International Communications in Heat and Mass Transfer, 27(2), 211–220. https://doi.org/10.1016/S0735-1933(00)00102-0
   Web of Science ®Google Scholar
• Peregrine, D. H. (1972). Equations for water waves and the approximations behind them. In R. E. Meyer (Ed.), Waves on beaches and resulting sediment transport (pp. 95–121). Academic Press.
   Google Scholar
• Pokrajac, D., & Kikkert, G. (2011). RADINS equations for aerated shallow water flows over rough beds. Journal of Hydraulic Research, 49(5), 630–638. https://doi.org/10.1080/00221686.2011.597940
   Web of Science ®Google Scholar
• Pokrajac, D., McEwan, I., & Nikora, V. (2008). Spatially averaged turbulent stress and its partitioning. Experiments in Fluids, 45(1), 73–83. https://doi.org/10.1007/s00348-008-0463-y
   Web of Science ®Google Scholar
• Roberts, S., Nielsen, O., Gray, D., & Sexton, J. (2009). ANUGA user manual 2.0. Geoscience Australia.
   Google Scholar
• Savage, S. B., & Hutter, K. (1989). The motion of a finite mass of granular material down a rough incline. Journal of Fluid Mechanics, 199, 177–215. https://doi.org/10.1017/S0022112089000340
   Web of Science ®Google Scholar
• Stansby, P. K., & Feng, T. (2005). Kinematics and depth-integrated terms in surf zone waves from laboratory measurement. Journal of Fluid Mechanics, 529, 279–310. https://doi.org/10.1017/S0022112005003599
   Web of Science ®Google Scholar
• Stoker, J. J. (1957). Water waves: The mathematical theory with applications. John Willey & Sons Inc.
   Google Scholar
• Toro, E. F. (2001). Shock-capturing methods for free-surface shallow flows. John Wiley & Sons.
   Google Scholar
• Ungarish, M. (2007). Axisymmetric gravity currents at high Reynolds number: On the quality of shallow-water modeling of experimental observations. Physics of Fluids, 19(3), Article 036602. https://doi.org/10.1063/1.2714990
   Google Scholar
• Volz, C., Rousselot, P., Vetsch, D., & Faeh, R. (2012). Numerical modelling of non-cohesive embankment breach with the dual-mesh approach. Journal of Hydraulic Research, 50(6), 587–598. https://doi.org/10.1080/00221686.2012.732970
   Web of Science ®Google Scholar
• Wang, G., Liang, Q., Shi, F., & Zheng, J. (2021). Analytical and numerical investigation of trapped ocean waves along a submerged ridge. Journal of Fluid Mechanics, 915, Article A54. https://doi.org/10.1017/jfm.2020.1039
   Google Scholar
• Whitham, G. B. (1974). Linear and nonlinear waves. John Willey & Sons Inc.
   Google Scholar
• Wilson, N. R., & Shaw, R. H. (1977). A higher order closure model for canopy flow. Journal of Applied Meteorology, 16, 1197–1205. https://doi.org/10.1175/1520-0450(1977)016¡1197:AHOCMF¿2.0.CO;2
   Google Scholar
• Wuppukondur, A., & Baldock, T. E. (2022). Physical and numerical modelling of representative tsunami waves propagating and overtopping in converging channels. Coastal Engineering, 174, Article 104120. https://doi.org/10.1016/j.coastaleng.2022.104120
   Google Scholar
• Xiong, Y., Mahaffey, S., Liang, Q., Rouainia, M., & Wang, G. (2020). A new 1D coupled hydrodynamic discrete element model for floating debris in violent shallow flows. Journal of Hydraulic Research, 58(5), 778–789. https://doi.org/10.1080/00221686.2019.1671513
   Web of Science ®Google Scholar
• Yu, H. L., & Chang, T. J. (2021). A hybrid shallow water solver for overland flow modelling in rural and urban areas. Journal of Hydrology, 598, Article 126262. https://doi.org/10.1016/j.jhydrol.2021.126262
   Google Scholar
• Zilitinkevich, S. S., Elperin, T., Kleeorin, N., LV́ov, V., & Rogachevskii, I. (2009). Energy- and flux-budget turbulence closure model for stably stratified flows. Part II: The role of internal gravity waves. Boundary-Layer Meteorology, 133(2), 139–164. https://doi.org/10.1007/s10546-009-9424-0
   Web of Science ®Google Scholar