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Shallow water equations for equatorial tsunami waves. [PDF]
Philos Trans A Math Phys Eng Sci, 2018 We present derivations of shallow water model equations of Korteweg–de Vries and Boussinesq type for equatorial tsunami waves in the f -plane approximation and discuss their applicability. This article is part of the theme issue ‘Nonlinear water waves’.
Geyer A, Quirchmayr R.
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Solving global shallow water equations on heterogeneous supercomputers. [PDF]
PLoS ONE, 2017 The scientific demand for more accurate modeling of the climate system calls for more computing power to support higher resolutions, inclusion of more component models, more complicated physics schemes, and larger ensembles. As the recent improvements in
Haohuan Fu +7 more
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Invariant Discretization Schemes for the Shallow-Water Equations [PDF]
SIAM Journal of Scientific Computing, 2012 27 pages, 6 figures, minor ...
Alexander Bihlo, Roman Popovych
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On a shallow water wave equation [PDF]
Nonlinearity, 1994 In this paper we study a shallow water equation derivable using the Boussinesq approximation, which includes as two special cases, one equation discussed by Ablowitz et. al. [Stud. Appl. Math., 53 (1974) 249--315] and one by Hirota and Satsuma [J. Phys. Soc. Japan}, 40 (1976) 611--612]. A catalogue of classical and nonclassical symmetry reductions, and
Clarkson, Peter A. +1 more
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Journal of Hydroinformatics, 2023 This paper proposes a novel energy-balanced numerical scheme for the two-layer shallow water equations (2LSWEs) that accurately captures internal hydraulic jumps without introducing spurious oscillations. The proposed scheme overcomes the problem of post-
Majid Akbari, Bahareh Pirzadeh
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Projective Integration for Hyperbolic Shallow Water Moment Equations
Axioms, 2022 In free surface flows, shallow water models simplify the flow conditions by assuming a constant velocity profile over the water depth. Recently developed Shallow Water Moment Equations allow for variations of the velocity profile at the expense of a more
Amrita Amrita, Julian Koellermeier
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Lubrication and shallow-water systems Bernis-Friedman and BD entropies [PDF]
ESAIM: Proceedings and Surveys, 2020 This paper concerns the results recently announced by the authors, in C.R. Acad. Sciences Maths volume 357, Issue 1, 1-6 (2019), which make the link between the BD entropy introduced by D. Bresch and B.
Bresch Didier +4 more
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Frontiers in Physics, 2023 Determining the non-linear traveling or soliton wave solutions for variable-order fractional evolution equations (VO-FEEs) is very challenging and important tasks in recent research fields.
Umair Ali +5 more
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A gauge theory for shallow water
SciPost Physics, 2023 The shallow water equations describe the horizontal flow of a thin layer of fluid with varying height. We show that the equations can be rewritten as a $d=2+1$ dimensional Abelian gauge theory.
David Tong
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Topology of rotating stratified fluids with and without background shear flow
Physical Review Research, 2023 Poincaré inertio-gravity modes described by the shallow water equations in a rotating frame have nontrivial topology, providing a perspective on the origin of equatorially trapped Kelvin and Yanai waves.
Ziyan Zhu, Christopher Li, J. B. Marston
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