- PII
- 10.31857/S0032823524030055-1
- DOI
- 10.31857/S0032823524030055
- Publication type
- Article
- Status
- Published
- Authors
- Volume/ Edition
- Volume 88 / Issue number 3
- Pages
- 406-421
- Abstract
- In the linear approximation of the surface gravitational waves of small amplitude a classical model problem about the incursion of a surface wave under some angle on the shoreline is solved. The problem is formulated for the harmonic potential of velocity of the fluid in the 3D water wedge with the Robin-Steklov boundary condition on the free surface and with the no-flow condition along the normal on the bed of the water domain. Some critical comments about a known in the literature solution having a “non-physical” singularity of the logarithmic type on the coastal line are given. The asymptotics with respect to distance from the shoreline of the obtained solution, bounded on the edge, is constructed. The reflection coefficient of the wave reflected from the shoreline is calculated.
- Keywords
- поверхностная волна интегральные представления функциональные уравнения асимптотика
- Date of publication
- 01.03.2024
- Year of publication
- 2024
- Number of purchasers
- 0
- Views
- 27
References
- 1. Shrira V.I. et al. Can edge waves be generated by wind? // J. of Fluid Mech. 2022. V. 934. P. A16–136.
- 2. Ehrenmark U.T. Oblique wave incidence on a plane beach: The classical problem revisited // J. of Fluid Mech. 1998. V. 368. P. 291–319.
- 3. Isaacson E. Water waves over a sloping bottom // Commun. Pure Appl. Maths. 1950. V. 3. P. 11–31.
- 4. Kuznetsov N., Mazya V., Vainberg B. Linear Water Waves. Cambridge: Univ. Press, 2002. 513 p.
- 5. Ursell F. Edge waves on a sloping beach // Proc. R. Soc. Lond. Ser. A. 1952. V. 214. P. 79–97.
- 6. Лялинов М.А. Комментарий о собственных функциях и собственных числах оператора Лапласа в угле с краевыми условиями Робэна // Зап. науч. сем. Санкт-Петербургского отд. математического института им. В.А. Стеклова РАН. 2019. Т. 483. №49. C. 116–127.
- 7. Khalile M., Pankrashkin K. Eigenvalues of Robin Laplacians in infinite sectors // Math. Nachrichten. 2018. V. 291. №5–6. P. 928–965.
- 8. Lyalinov M.A. Eigenoscillations in an angular domain and spectral properties of functional equations // Europ. J. of Appl. Math. 2021. V. 33. P. 538–559.
- 9. Лялинов М.А. О собственных функциях существенного спектра модельной задачи для оператора Шрёдингера с сингулярным потенциалом // Матем. сб. 2023. Т. 214(10). C. 3–29.
- 10. Babich V.M., Lyalinov M.A., Grikurov V.E. Diffraction Theory: The Sommerfeld–Malyuzhinets Technique. Oxford: Alpha Sci. Int., 2008. 215 p.
- 11. Малюжинец Г.Д. Возбуждение, отражение и излучение поверхностных волн от клина с произвольными поверхностными импедансами // Докл. АН СССР. 1985. Т. 3. С. 752–55.
- 12. Gradshteyn I.S., Ryzhik M.I. Table of Integrals. Series, and Products. New York: Acad. Press, 2007. 1108 p.
- 13. Lyalinov M.A. Functional difference equations and and their link with perturbations of the Mehler operator // Rus. J. of Math. Phys. 2022. V. 29. №3. P. 379–397.
