Email this article Simple solutions to the wave problem on the surface of a fluid with the linear hydroelastic model
- Authors: Dobrokhotov S.Y.1,2, Il’yasov K.K.1, Sekerzh-Zen’kovich S.Y.1, Tolstova O.L.2,3
-
Affiliations:
- Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
- Moscow Institute of Physics and Technology
- Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 487, No 4 (2019)
- Pages: 370-375
- Section: Mechanics
- URL: https://journals.eco-vector.com/0869-5652/article/view/15822
- DOI: https://doi.org/10.31857/S0869-56524874370-375
- ID: 15822
Cite item
Full Text
Abstract
The problem of generation of waves on the surface of a water layer placed on an elastic base is considered. It is assumed that the generating source is located inside the elastic half-space. The Podyapolskii approach is used which is based on study of the solutions to the common linear system of equations of the theory of elasticity in the half-space and the theory of water waves linked at the interface by the corresponding boundary conditions. The previously obtained simplified dispersion relation for the water mode with account for the elastic base effect is used to derive a simple integral formula which associates the initial perturbation of a special kind in the elastic half-space and the amplitude of the surface water waves generated by this source. The obtained solutions are compared with the solutions based on the well-known piston model of long wave generation.
About the authors
S. Yu. Dobrokhotov
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences; Moscow Institute of Physics and Technology
Email: ilyasov@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526; 9, Institutskij, Dolgoprudny, Moscow region, 141701
Kh. Kh. Il’yasov
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Author for correspondence.
Email: ilyasov@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526
S. Ya. Sekerzh-Zen’kovich
Ishlinsky Institute for Problems in Mechanics of the Russian Academy of Sciences
Email: ilyasov@ipmnet.ru
Russian Federation, 101, bldg. 1, Vernadskogo prospect, Moscow, 119526
O. L. Tolstova
Moscow Institute of Physics and Technology; Steklov Mathematical Institute of Russian Academy of Sciences
Email: olga111@rambler.ru
Russian Federation, 9, Institutskij, Dolgoprudny, Moscow region, 141701; 8, Gubkina street, Moscow, 117966
References
- Пелиновский Е. Н. Гидродинамика волн цунами. Н. Новгород: Ин-т прикладной физики РАН, 1996.
- Kanamori H. // Phys. Earth and Planet. Inter. 1972. № 6. P. 349-359.
- Yamashita T., Sato R. // J. Phys. Earth. 1974. № 22. P. 415-440.
- Подъяпольский Г. С. В cб.: Методы расчета возникновения и распространения цунами. М.: Наука, 1978.
- Sabatier P. C. // J. Fluid Mech. 1983. V. 126. P. 27-58.
- Гусяков В. К., Чубаров Л. Б. // Изв. РАН. Физика Земли. 1987. В. 11. C. 53-64.
- Фрагела А. К. // Дифференц. уравнения. 1989. Т. 25. В. 8. C. 1417-1426.
- Доброхотов С. Ю., Толстова О. Л., Чудинович И. Ю. // Мат. заметки. 1993. Т. 54. В. 3. C. 33-55.
- Гринив Р. О., Доброхотов С. Ю., Шкаликов А. А. // Мат. заметки. 2000. Т. 68. В. 1. C. 57-70.
- Зволинский Н. В., Карпов И. И., Никитин И. С., Секерж-Зенькович С.Я. // Изв. РАН. Физика Земли. 1994. В. 9. C. 29-33.
- Dobrokhotov S.Yu., Tolstova O. L., Sekerzh-Zenko-vich S.Ya., Vargas C. A. // Russ. J. Math. Phys. 2018. V. 25. № 4. P. 459-469.
- Dobrokhotov S.Yu., Nazaikinskii V. E., Tirozzi B. // Russ. J. Math. Phys. 2010. V. 17. № 1. P. 66-76.
- Федорюк М. В. Асимптотика, интегралы и ряды. М.: Наука, 1987.
- Wolfram Mathematica. www.wolfram.com/mathematica/
Supplementary files
