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Issue 9, 2026
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Gerstner waves and their generalizations in hydrodynamics and geophysics

†  a, b, ‡  a, c, b
a Federal Research Center A.V. Gaponov-Grekhov Institute of Applied Physics of the Russian Academy of Sciences, ul. Ulyanova 46, Nizhny Novgorod, 603000, Russian Federation
b National Research University Higher School of Economics, Nizhny Novgorod Branch, B. Pecherskaya str. 25/12, Nizhny Novgorod, 603155, Russian Federation
c Alexeev 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).

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Fulltext is also available at DOI: 10.3367/UFNe.2021.05.038980
Correspondence should be addressed to
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/
001112520100003
2-s2.0-85160618208
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, 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

References (112) Cited by (16) Similar articles (20) ↓

  1. A.A. Abrashkin, E.N. Pelinovsky “On the relation between Stokes drift and the Gerstner wave” Phys. Usp. 61 307–312 (2018)
  2. G.S. Golitsyn “A N Kolmogorov's 1934 paper is the basis for explaining the statistics of natural phenomena of the macrocosm” Phys. Usp. 67 80–90 (2024)
  3. B.Ya. Shmerlin, M.V. Kalashnik “Rayleigh convective instability in the presence of phase transitions of water vapor. The formation of large-scale eddies and cloud structures” Phys. Usp. 56 473–485 (2013)
  4. P.N. Svirkunov, M.V. Kalashnik “Phase patterns of dispersive waves from moving localized sources” Phys. Usp. 57 80–91 (2014)
  5. D.S. Agafontsev, E.A. Kuznetsov et al “Compressible vortex structures and their role in the onset of hydrodynamic turbulence” Phys. Usp. 65 189–208 (2022)
  6. A.M. Gaifullin, V.V. Zhvick “Laminar submerged jets of incompressible fluid at large Reynolds numbers” Phys. Usp. 66 1142–1153 (2023)
  7. E.N. Rumanov “Critical phenomena far from equilibrium” Phys. Usp. 56 93–102 (2013)
  8. A.V. Borisov, A.O. Kazakov, S.P. Kuznetsov “Nonlinear dynamics of the rattleback: a nonholonomic model” Phys. Usp. 57 453–460 (2014)
  9. G.I. Broman, O.V. Rudenko “Submerged Landau jet: exact solutions, their meaning and application” Phys. Usp. 53 91–98 (2010)
  10. M.V. Kuzelev, A.A. Rukhadze “Waves in inhomogeneous plasmas and liquid and gas flows. Analogies between electro- and gas-dynamic phenomena” Phys. Usp. 61 748–764 (2018)
  11. V.N. Tsytovich “On the physical interpretation of Thomson scattering in a plasma” Phys. Usp. 56 180–191 (2013)
  12. D.A. Shalybkov “Hydrodynamic and hydromagnetic stability of the Couette flow” Phys. Usp. 52 915–935 (2009)
  13. N.V. Selina “Light diffraction in a plane-parallel layered structure with the parameters of a Pendry lens” Phys. Usp. 65 406–414 (2022)
  14. E.H. Lock, S.V. Gerus “Electromagnetic waves in a tangentially magnetized bi-gyrotropic layer (with an example of analysis of spin wave characteristics in a ferrite plate)” Phys. Usp. 67 1257–1270 (2024)
  15. S.F. Garanin, S.D. Kuznetsov “Irrotational flow (of a magnetic field or incompressible fluid) around a screen with a slot” Phys. Usp. 63 1037–1042 (2020)
  16. V.V. Vasiliev, L.V. Fedorov “Spherically symmetric static problem of General Relativity for a continuum” Phys. Usp. 68 187–202 (2025)
  17. A.V. Vashkovsky, E.H. Lock “On the relationship between magnetostatic wave energy and dispersion characteristics in ferrite structures” Phys. Usp. 54 281–290 (2011)
  18. M.V. Kuzelev, A.A. Rukhadze “Nonrelativistic quantum theory of stimulated Cherenkov radiation and Compton scattering in a plasma” Phys. Usp. 54 375–380 (2011)
  19. A.A. Shatskii, I.D. Novikov, N.S. Kardashev “A dynamic model of the wormhole and the Multiverse model” Phys. Usp. 51 457–464 (2008)
  20. G.S. Golitsyn “Demonstrativeness of using energy rather than mass as the unit of measure for a number of problems in physics, mechanics, and geophysics” Phys. Usp. 51 723–725 (2008)

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