Next Article in Journal
Effects of Secondary Currents on Turbulence Characteristics of Supercritical Open Channel Flows at Low Aspect Ratios
Previous Article in Journal
Glacier Mapping Based on Random Forest Algorithm: A Case Study over the Eastern Pamir
Previous Article in Special Issue
Dam Break Modeling in a Cascade of Small Earthen Dams: Case Study of the Čižina River in the Czech Republic
Article

Vertically Averaged and Moment Equations for Dam-Break Wave Modeling: Shallow Water Hypotheses

1
Soil and Water Division, IAS-CSIC, Spanish National Research Council, Alameda del Obispo s/n, 14004 Córdoba, Spain
2
Hydraulic Engineering Area, Rabanales Campus, Leonardo da Vinci Building, University of Cordoba, 14071 Córdoba, Spain
3
Water and Environmental Engineering Research Team (GEAMA), Civil Engineering School, Universidade da Coruña, Elviña, 15071 Coruña, Spain
4
Laboratory of Hydraulics, Hydrology and Glaciology, Swiss Federal Institute of Technology, 8093 Zürich, Switzerland
*
Author to whom correspondence should be addressed.
Water 2020, 12(11), 3232; https://doi.org/10.3390/w12113232
Received: 14 October 2020 / Revised: 13 November 2020 / Accepted: 16 November 2020 / Published: 18 November 2020
The dam-break wave modeling technology relies upon the so-called shallow water equations (SWE), i.e., mass and momentum vertically averaged equations by implementing the shallow water hypotheses, namely (i) horizontal velocity component independent of the vertical coordinate, (ii) vertical velocity component is null, (iii) pressure distribution is hydrostatic, (iv) turbulence is neglected. While this model often yields a satisfactory answer from an engineering standpoint, flows with vertical length scales not negligible cannot be modeled with accuracy, including the undular surge generated after a dam break for relatively high tailwater levels. These flows are modeled by the Serre–Green–Naghdi equations (SGNE), which fail to mimic wave breaking for low tailwater levels, however. Neither SWE nor SGNE produce a fully satisfactory answer for modeling dam break waves, therefore. A higher-order model using vertically averaged and moment equations (VAM) is used in this work to simulate dam break waves, thereby showing good results for arbitrary values of the tailwater level. The model contains four perturbation parameters implemented to overcome the shallow water hypotheses; two for the velocity components and two for fluid pressure. The role of each parameter in relaxing the limitations of the SWE is systematically investigated, depicting a complex and necessary interplay between the dynamic component of fluid pressure and the modeling of the velocity profile in producing accurate solutions for both non-hydrostatic and broken waves in dam break flows. The results highlight how the shallow water hypotheses can be relaxed in the vertically averaged modeling of dam break waves, producing an outcome of both theoretical and practical interest in the field. The results generated are tested with available experimental data, resulting in acceptable agreement. View Full-Text
Keywords: dam break; non-hydrostatic flow; shallow water hypotheses; vertically averaged model; weighted residual method dam break; non-hydrostatic flow; shallow water hypotheses; vertically averaged model; weighted residual method
Show Figures

Figure 1

MDPI and ACS Style

Cantero-Chinchilla, F.N.; Bergillos, R.J.; Gamero, P.; Castro-Orgaz, O.; Cea, L.; Hager, W.H. Vertically Averaged and Moment Equations for Dam-Break Wave Modeling: Shallow Water Hypotheses. Water 2020, 12, 3232. https://doi.org/10.3390/w12113232

AMA Style

Cantero-Chinchilla FN, Bergillos RJ, Gamero P, Castro-Orgaz O, Cea L, Hager WH. Vertically Averaged and Moment Equations for Dam-Break Wave Modeling: Shallow Water Hypotheses. Water. 2020; 12(11):3232. https://doi.org/10.3390/w12113232

Chicago/Turabian Style

Cantero-Chinchilla, Francisco N.; Bergillos, Rafael J.; Gamero, Pedro; Castro-Orgaz, Oscar; Cea, Luis; Hager, Willi H. 2020. "Vertically Averaged and Moment Equations for Dam-Break Wave Modeling: Shallow Water Hypotheses" Water 12, no. 11: 3232. https://doi.org/10.3390/w12113232

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Search more from Scilit
 
Search
Back to TopTop