The one-dimensional Green–Naghdi equations with a time dependent bottom topography and their conservation laws
| Autor: | E. I. Kaptsov, Sergey V. Meleshko, N. F. Samatova |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Fluid Flow and Transfer Processes
Physics Conservation law Group (mathematics) Mechanical Engineering Mathematical analysis Computational Mechanics Eulerian path Condensed Matter Physics 01 natural sciences 010305 fluids & plasmas Physics::Fluid Dynamics symbols.namesake Lagrangian and Eulerian specification of the flow field Mechanics of Materials Complete group 0103 physical sciences symbols Fluid dynamics Noether's theorem 010306 general physics Physics::Atmospheric and Oceanic Physics Lagrangian |
| Zdroj: | Physics of Fluids. 32:123607 |
| ISSN: | 1089-7666 1070-6631 |
| DOI: | 10.1063/5.0031238 |
| Popis: | This paper deals with the one-dimensional Green–Naghdi equations describing the behavior of fluid flow over an uneven bottom topography depending on time. Using Matsuno’s approach, the corresponding equations are derived in Eulerian coordinates. Further study is performed in Lagrangian coordinates. This study allowed us to find the general form of the Lagrangian corresponding to the analyzed equations. Then, Noether’s theorem is used to derive conservation laws. As some of the tools in the application of Noether’s theorem are admitted generators, a complete group classification of the Green–Naghdi equations with respect to the bottom depending on time is performed. Using Noether’s theorem, the found Lagrangians, and the group classification, conservation laws of the one-dimensional Green–Naghdi equations with uneven bottom topography depending on time are obtained. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|