Flow of shallow water with a periodic system of jumps over a vertical surface
| Autor: | V. A. Buchin, G. A. Shaposhnikova |
|---|---|
| Rok vydání: | 2009 |
| Předmět: |
Physics
Work (thermodynamics) Computational Mechanics General Physics and Astronomy Mechanics Viscous liquid Physics::Fluid Dynamics Surface tension Nonlinear system Exact solutions in general relativity Flow (mathematics) Mechanics of Materials Constant (mathematics) Hyperbolic partial differential equation |
| Zdroj: | Doklady Physics. 54:248-251 |
| ISSN: | 1562-6903 1028-3358 |
| DOI: | 10.1134/s1028335809050073 |
| Popis: | A problem of the flow of a thin layer of viscous fluid over a vertical surface is considered. The problem is solved in the approximation of shallow water, and the surface tension is neglected. In this approximation, the nonsteady flow of a thin layer is described by a set of nonlinear hyperbolic equations. It is known that the simplest steady flow with constant parameters is unstable. The development of perturbations leads to a nonuniform limited flow, which can involve the jumps. It is of interest to find the solutions containing the jumps. In the case if the perturbations introduced into the flow are periodic, we can expect that the solution with the jumps will also be periodic. In this work, we constructed an exact solution of the problem of the flow of shallow water with a periodic system of jumps moving with a constant velocity downward along the flow. The distance between the jumps is a free parameter. The solution is obtained in the explicit form. |
| Databáze: | OpenAIRE |
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