Publication Cover
Applicable Analysis
An International Journal
Volume 103, 2024 - Issue 5
97
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On some recently derived exact solutions to the Euler equations

& ORCID Icon
Pages 998-1007 | Received 06 Nov 2022, Accepted 04 Jun 2023, Published online: 09 Jun 2023

References

  • Chu J. On a nonlinear integral equation for the ocean flow in arctic gyres. Quart Appl Math. 2018;76(3):489–498. doi: 10.1090/qam/2018-76-03
  • Chu J. On a nonlinear model for arctic gyres. Ann Mat Pura Appl (4). 2018;197(3):651–659. doi: 10.1007/s10231-017-0696-6
  • Constantin A. Nonlinear wind-drift ocean currents in arctic regions. Geophys Astrophys Fluid Dyn. 2022;116(2):101–115. doi: 10.1080/03091929.2021.1981307
  • Constantin A. Comments on: nonlinear wind-drift ocean currents in arctic regions. Geophys Astrophys Fluid Dyn. 2022;116(2):116–121. doi: 10.1080/03091929.2022.2036337
  • Constantin A. An exact solution for equatorially trapped waves. J Geophys Res Oceans. 2012;117(C5):Article ID C05029. doi: 10.1029/2012JC007879
  • Cushman-Roisin B, Beckers JM. Introduction to geophysical fluid dynamics: physical and numerical aspects. Waltham, Mass.: Academic; 2011.
  • Ionescu-Kruse D. An exact solution for geophysical edge waves in the f-plane approximation. Nonlinear Anal Real World Appl. 2015;24:190–195. doi: 10.1016/j.nonrwa.2015.02.002
  • Pollard RT. Surface waves with rotation: an exact solution. J Geophys Res. 1970;75(30):5895–5898. doi: 10.1029/JC075i030p05895
  • Constantin A, Germain P. On the open sea propagation of water waves generated by a moving bed. Philos Trans R Soc Lond Ser A Math Phys Eng Sci. 2012;370(1964):1587–1601. doi:10.1098/rsta.2011.0443
  • Henry D. Equatorially trapped nonlinear water waves in a β-plane approximation with centripetal forces. J Fluid Mech. 2016;804:R11–R111. doi: 10.1017/jfm.2016.544
  • Gerstner F. Theorie der Wellen samt einer daraus abgeleiteten theorie der deichprofile. Ann Phys. 1809;32(8):412–445. doi: 10.1002/(ISSN)1521-3889
  • Froude W. On the rolling of ships. Trans R Inst Naval Arch. 1862;3:45–62.
  • Rankine WJM. On the exact form of waves near the surface of deep water. Philos Trans R Soc Lond A. 1863;153:127–138.
  • Constantin A. On the modelling of equatorial waves. Geophys Res Lett. 2012;39(5):Article ID L05602. doi: 10.1029/2012GL051169
  • Constantin A. Some three-dimensional nonlinear equatorial flows. J Phys Oceanogr. 2013;43(1):165–175. doi: 10.1175/JPO-D-12-062.1
  • Constantin A. Some nonlinear, equatorially trapped, nonhydrostatic internal geophysical waves. J Phys Oceanogr. 2014;44(2):781–789. doi: 10.1175/JPO-D-13-0174.1
  • Constantin A, Monismith SG. Gerstner waves in the presence of mean currents and rotation. J Fluid Mech. 2017;820:511–528. doi: 10.1017/jfm.2017.223
  • Constantin A. On the deep water wave motion. J Phys A. 2001;34(7):1405–1417. doi: 10.1088/0305-4470/34/7/313
  • Henry D. On Gerstner's water wave. J Nonlinear Math Phys. 2008;15:87–95. doi: 10.2991/jnmp.2008.15.s2.7
  • Henry D. On three-dimensional Gerstner-like equatorial water waves. Philos Trans Roy Soc A. 2018;376(2111) 16. Article ID 20170088. doi: 10.1098/rsta.2017.0088
  • Henry D. An exact solution for equatorial geophysical water waves with an underlying current. Eur J Mech B Fluids. 2013;38:18–21. doi: 10.1016/j.euromechflu.2012.10.001
  • Matioc AV. On the particle motion in geophysical deep water waves traveling over uniform currents. Quart Appl Math. 2014;72(3):455–469. doi: 10.1090/qam/2014-72-03
  • Chu J, Ionescu-Kruse D, Yang Y. Exact solution and instability for geophysical trapped waves at arbitrary latitude. Discrete Contin Dyn Syst. 2019;39(8):4399–4414. doi: 10.3934/dcds.2019178
  • Chu J, Ionescu-Kruse D, Yang Y. Exact solution and instability for geophysical waves with centripetal forces and at arbitrary latitude. J Math Fluid Mech. 2019;21(2):Article ID 19, 16 pp. doi: 10.1007/s00021-019-0423-8
  • Ionescu-Kruse D. An exact solution for geophysical edge waves in the β-plane approximation. J Math Fluid Mech. 2015;17(4):699–706. doi: 10.1007/s00021-015-0233-6
  • Ionescu-Kruse D. Exact steady azimuthal edge waves in rotating fluids. J Math Fluid Mech. 2017;19(3):501–513. doi: 10.1007/s00021-016-0287-0
  • Matioc AV. An exact solution for geophysical equatorial edge waves over a sloping beach. J Phys A. 2012;45(36):Article ID 365501. doi: 10.1088/1751-8113/45/36/365501
  • Matioc AV. Exact geophysical waves in stratified fluids. Appl Anal. 2013;92(11):2254–2261. doi: 10.1080/00036811.2012.727987
  • Martin CI. Some explicit solutions to the three-dimensional nonlinear water wave problem. J Math Fluid Mech. 2021;23(2):8 pp. doi: 10.1007/s00021-021-00564-4
  • Henry redD, Martin CI. Exact, free-surface equatorial flows with general stratification in spherical coordinates. Arch Ration Mech Anal. 2019;233(1):497–512. doi: 10.1007/s00205-019-01362-z
  • Martin CI. Azimuthal equatorial flows in spherical coordinates with discontinuous stratification. Phys Fluids. 2021;33(2):Article ID 026602. doi: 10.1063/5.0035443
  • Martin CI, Quirchmayr R. Exact solutions and internal waves for the antarctic circumpolar current in spherical coordinates. Stud Appl Math. 2022;148(3):1021–1039. doi: 10.1111/sapm.v148.3
  • Martin CI. Some explicit solutions of the three-dimensional Euler equations with a free surface. Math Ann. 2022;384(3-4):1653–1673. doi: 10.1007/s00208-021-02323-2
  • Constantin A, Johnson RS. A nonlinear, three-dimensional model for ocean flows. Phys Fluids. 2017;29(5):Article ID 056604. doi: 10.1063/1.4984001
  • Constantin A, Johnson RS. On the nonlinear, three-dimensional structure of equatorial oceanic flows. J Phys Oceanogr. 2019;49(8):2029–2042. doi: 10.1175/JPO-D-19-0079.1
  • Constantin A. Nonlinear water waves with applications to wave-current interactions and tsunamis. In: CBMS-NSF conference series in applied mathematics. Vol. 81; SIAM. Philadelphia; 2011.
  • Johnson RS. Models for the formation of a critical layer in water wave propagation. Philos Trans R Soc A Math Phys Eng Sci. 2012;370(1964):1638–1660. doi: 10.1098/rsta.2011.0456
  • Overland JE. Providing winds for wave models. Ocean wave climate; 1979. p. 3–37.
  • Constantin A, Ivanov RI. A Hamiltonian approach to wave-current interactions in two-layer fluids. Phys Fluids. 2015;27(8):Article ID 086603. doi: 10.1063/1.4929457
  • Constantin A, Ivanov RI. Equatorial wave–current interactions. Comm Math Phys. 2019;370(1):1–48. doi: 10.1007/s00220-019-03483-8
  • Constantin A, Ivanov RI, Martin CI. Hamiltonian formulation for wave-current interactions in stratified rotational flows. Arch Ration Mech Anal. 2016;221(3):1417–1447. doi: 10.1007/s00205-016-0990-2

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.