 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10482 |
| In Russian (ΟΜΜ): | | 9683
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| In English (J. Appl. Math. Mech.): | | 799 |
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| A.A. Chesnokov, "Properties and exact solutions of the equations of motion of shallow water in a spinning paraboloid," J. Appl. Math. Mech. 75 (3), 350-356 (2011) |
| Year |
2011 |
Volume |
75 |
Issue |
3 |
Pages |
350-356 |
| Title |
Properties and exact solutions of the equations of motion of shallow water in a spinning paraboloid |
| Author(s) |
A.A. Chesnokov (Novosibirsk, Russia, chesnokov@hydro.nsc.ru) |
| Abstract |
A transformation is found and, using this, the non-linear system of equations describing the spatial oscillations of a thin layer of liquid in a spinning circular parabolic basin is reduced to the conventional equations of the model of shallow water over a level fixed bottom. This transformation is obtained by analyzing the properties of the symmetry of the equations of motion of spinning shallow water. The existence of non-trivial symmetries in the case of the model considered enabled group multiplication of the solutions to be carried out. Using the known steady-state rotationally symmetric solution, a class of time-periodic solutions is obtained that describes the non-linear oscillations of the liquid in a circular paraboloid with closed or quasiclosed (ergodic) trajectories of the motion of the liquid particles. |
| Received |
15 June 2009 |
| Link to Fulltext |
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