Gerstner waves and their generalizations in hydrodynamics and geophysics

A.A. Abrashkin^†^a, b, E.N. Pelinovsky^‡^a, c, b
^aFederal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
^bNational Research University Higher School of Economics, Nizhny Novgorod Branch, B. Pecherskaya str. 25/12, Nizhny Novgorod, 603155, Russian Federation
^cAlexeev Nizhnii Novgorod State Technical University, Minina str. 24, Nizhnii Novgorod, 603600, Russian Federation

To mark 220 years since the appearance of Gerstner's paper that proposed an exact solution to the hydrodynamic equations, an overview of exact solutions for water waves is given, each of which is a generalization of the Gerstner wave. Additional factors are coastal geometry, fluid rotation, varying pressure on the free surface, stratification, fluid compressibility, and background flows. Waves on a rotating Earth are studied in the f-plane approximation, and, in the near-equatorial region, also in the β-plane approximation. The flows are described in Lagrangian variables. For all waves in the absence of background flows, the trajectories of liquid particles are circles, as in the Gerstner wave (hence, their common name—Gerstner-like).

Keywords: Gerstner waves, Lagrangian coordinates, vorticity, Cauchy invariants, edge waves, Ptolemaic flows, rotating fluid, f-plane approximation, equatorially trapped waves
PACS: 47.35.Bb
DOI: 10.3367/UFNe.2021.05.038980
URL: https://ufn.ru/en/articles/2022/5/c/
Web of Science

001112520100003
Scopus

2-s2.0-85160618208
ADS NASA

2022PhyU...65..453A
Citation: Abrashkin A A, Pelinovsky E N "Gerstner waves and their generalizations in hydrodynamics and geophysics" Phys. Usp. 65 453–467 (2022)

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Received: 1st, February 2021, revised: 9th, April 2021, accepted: 3rd, May 2021

Оригинал: Абрашкин А А, Пелиновский Е Н «Волны Герстнера и их обобщения в гидродинамике и геофизике» УФН 192 491–506 (2022); DOI: 10.3367/UFNr.2021.05.038980

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