✦ LIBER ✦

On symmetries and conservation laws of the equations of shallow water with an axisymmetric profile of bottom

✍ Scribed by V. S. Titov

Publisher: Springer Netherlands
Year: 1989
Tongue: English
Weight: 453 KB
Volume: 15
Category: Article
ISSN: 0167-8019
DOI: 10.1007/bf00131933

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✦ Synopsis

The local symmetries and conservation laws are calculated for the equations of shallow water with an axisymmetric profile of bottom under the assumption that the corresponding generating functions may depend only on all variables and their derivatives up to the second order. It is shown that if the bottom has the form of a paraboloid of revolution, then there are many symmetries and conservation laws generalizing those for the case of plane bottom.

📜 SIMILAR VOLUMES

An inherently mass-conserving semi-impli

An inherently mass-conserving semi-implicit semi-Lagrangian discretisation of the shallow-water equations on the sphere

✍ M. Zerroukat; N. Wood; A. Staniforth; A. A. White; J. Thuburn 📂 Article 📅 2009 🏛 John Wiley and Sons 🌐 English ⚖ 674 KB

## Abstract For the shallow‐water equations on the sphere, an inherently mass‐conserving semi‐Lagrangian discretisation (SLICE) of the continuity equation is coupled with a semi‐implicit semi‐Lagrangian discretisation of the momentum equations. Various tests from the literature (two with analytical