Jeschke, A. and Pedersen, G.K. and Vater, S. and Behrens, J.
(2017)
*Depth‐averaged non‐hydrostatic extension for shallow water equations with quadratic vertical pressure profile: equivalence to Boussinesq‐type equations.*
International Journal for Numerical Methods in Fluids, 84
(109710).
pp. 569-583.
ISSN 1097-0363

Full text not available from this repository.

Official URL: https://doi.org/10.1002/fld.4361

## Abstract

We reformulate the depth‐averaged non‐hydrostatic extension for shallow water equations to show equivalence with well‐known Boussinesq‐type equations. For this purpose, we introduce two scalars representing the vertical profile of the non‐hydrostatic pressure. A specific quadratic vertical profile yields equivalence to the Serre equations, for which only one scalar in the traditional equation system needs to be modified. Equivalence can also be demonstrated with other Boussinesq‐type equations from the literature when considering variable depth, but then the non‐hydrostatic extension involves mixed space–time derivatives. In case of constant bathymetries, the non‐hydrostatic extension is another way to circumvent mixed space–time derivatives arising in Boussinesq‐type equations. On the other hand, we show that there is no equivalence when using the traditionally assumed linear vertical pressure profile. Linear dispersion and asymptotic analysis as well as numerical test cases show the advantages of the quadratic compared with the linear vertical non‐hydrostatic pressure profile in the depth‐averaged non‐hydrostatic extension for shallow water equations.

Item Type: | Article |
---|---|

Subjects: | Mathematical and Computer Sciences > Mathematics > Applied Mathematics |

Divisions: | Department of Mathematics and Computer Science > Institute of Mathematics > Geophysical Fluid Dynamics Group |

ID Code: | 2412 |

Deposited By: | Ulrike Eickers |

Deposited On: | 25 Feb 2020 14:25 |

Last Modified: | 25 Feb 2020 14:25 |

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