Discover the GLM and pseudo-Lagrangian equations of fluid dynamics on four pages
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918377370419200 |
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| author | Vladimirov, V. A. |
| author_facet | Vladimirov, V. A. |
| contents | The General Lagrangian Mean (GLM) theory uses a set of averaged equations of fluid dynamics to describe interactions between mean flows and waves. These equations are formulated in coordinates that follow the fluid's average velocity and are often referred to as `pseudo-Lagrangian' or `semi-Lagrangian'. This paper focuses on the principles for deriving the pseudo-Lagrangian and GLM equations, using an inviscid, incompressible, homogeneous fluid as a demonstration case. Our exposition differs methodically from that of others and is aimed at the learners of the subject.
Keywords: fluid flows, pseudo-Lagrangian description, GLM theory, inviscid incompressible fluid, Lagrangian displacements, mean flows, waves, averaged equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13237 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Discover the GLM and pseudo-Lagrangian equations of fluid dynamics on four pages Vladimirov, V. A. Fluid Dynamics Mathematical Physics 76A02 76B99 76M99 The General Lagrangian Mean (GLM) theory uses a set of averaged equations of fluid dynamics to describe interactions between mean flows and waves. These equations are formulated in coordinates that follow the fluid's average velocity and are often referred to as `pseudo-Lagrangian' or `semi-Lagrangian'. This paper focuses on the principles for deriving the pseudo-Lagrangian and GLM equations, using an inviscid, incompressible, homogeneous fluid as a demonstration case. Our exposition differs methodically from that of others and is aimed at the learners of the subject. Keywords: fluid flows, pseudo-Lagrangian description, GLM theory, inviscid incompressible fluid, Lagrangian displacements, mean flows, waves, averaged equations. |
| title | Discover the GLM and pseudo-Lagrangian equations of fluid dynamics on four pages |
| topic | Fluid Dynamics Mathematical Physics 76A02 76B99 76M99 |
| url | https://arxiv.org/abs/2601.13237 |