scholarly journals Zeroth‐order conservation laws of two‐dimensional shallow water equations with variable bottom topography

2020 ◽  
Vol 145 (2) ◽  
pp. 291-321
Author(s):  
Alexander Bihlo ◽  
Roman O. Popovych
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Two Dimensional ◽  
Zeroth Order ◽  
Variable Bottom

Long-time shallow-water equations with a varying bottom

1997 ◽  
Vol 349 ◽  
pp. 173-189 ◽  
Author(s):  
ROBERTO CAMASSA ◽  
DARRYL D. HOLM ◽  
C. DAVID LEVERMORE
Keyword(s):  
Conservation Laws ◽  
Shallow Water ◽  
Euler Equations ◽  
Shallow Water Equations ◽  
Bottom Topography ◽  
Three Dimensional ◽  
Local Conservation ◽  
First Order ◽  
Long Time ◽  
Conservation Laws Of Energy

We present and discuss new shallow-water equations that model the long-time effects of slowly varying bottom topography and weak hydrostatic imbalance on the vertically averaged horizontal velocity of an incompressible fluid possessing a free surface and moving under the force of gravity. We consider the regime where the Froude number ε is much smaller than the aspect ratio δ of the shallow domain. The new equations are obtained from the ε→0 limit of the Euler equations (the rigid-lid approximation) at the first order of an asymptotic expansion in δ2. These equations possess local conservation laws of energy and vorticity which reflect exact layer mean conservation laws of the three-dimensional Euler equations. In addition, they convect potential vorticity and have a Hamilton's principle formulation. We contrast them with the Green–Naghdi equations.

scholarly journals Modelling Weirs in Two-Dimensional Shallow Water Models

Water ◽  
2021 ◽  
Vol 13 (16) ◽  
pp. 2152
Author(s):  
Gonzalo García-Alén ◽  
Olalla García-Fonte ◽  
Luis Cea ◽  
Luís Pena ◽  
Jerónimo Puertas
Keyword(s):  
Experimental Data ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
Two Dimensional ◽  
Shallow Water Model ◽  
Experimental Dataset ◽  
River Hydraulics ◽  
Shallow Water Models ◽  
Water Models

2D models based on the shallow water equations are widely used in river hydraulics. However, these models can present deficiencies in those cases in which their intrinsic hypotheses are not fulfilled. One of these cases is in the presence of weirs. In this work we present an experimental dataset including 194 experiments in nine different weirs. The experimental data are compared to the numerical results obtained with a 2D shallow water model in order to quantify the discrepancies that exist due to the non-fulfillment of the hydrostatic pressure hypotheses. The experimental dataset presented can be used for the validation of other modelling approaches.

scholarly journals A two-dimensional high-order well-balanced scheme for the shallow water equations with topography and Manning friction

2021 ◽  
pp. 105152
Author(s):  
Victor Michel-Dansac ◽  
Christophe Berthon ◽  
Stéphane Clain ◽  
Françoise Foucher
Keyword(s):  
Shallow Water ◽  
Shallow Water Equations ◽  
High Order ◽  
Two Dimensional
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