Inertio-gravity Poincaré waves and the quantum relativistic Klein–Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation
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Publication date
2022-11
Authors
Heifetz, Eyal
Maas, L.R.M.
Mak, Julian
Pomerantz, Ishay
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Document Type
Article
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Abstract
Shallow water inertio-gravity Poincaré waves in a rotating frame satisfy the Klein-Gordon equation, originally derived for relativistic, spinless quantum particles. Here, we compare these two superficially unrelated phenomena, suggesting a reason for them sharing the same equation. We discuss their energy conservation laws and the equivalency between the non-relativistic limit of the Klein-Gordon equation, yielding the Schrödinger equation, and the near-inertial wave limit in the shallow water system.
Keywords
Propagation, Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering, Fluid Flow and Transfer Processes, Computational Mechanics, SDG 7 - Affordable and Clean Energy
Citation
Heifetz, E, Maas, L R M, Mak, J & Pomerantz, I 2022, 'Inertio-gravity Poincaré waves and the quantum relativistic Klein–Gordon equation, near-inertial waves and the non-relativistic Schrödinger equation', Physics of Fluids, vol. 34, no. 11, 116608, pp. 1-7. https://doi.org/10.1063/5.0120375