On the Propulsion of a Rigid Body in a Viscous Liquid by Time-Periodic Force with a Zero Average
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912668161409024 |
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| author | Edelmann, Joris Galdi, Giovanni P. Karakouzian, Mher M. Richter, Thomas |
| author_facet | Edelmann, Joris Galdi, Giovanni P. Karakouzian, Mher M. Richter, Thomas |
| contents | We perform analytical and numerical analyses of the propulsion of a rigid body in a viscous fluid subjected to a periodic force with zero average over a period. This general formulation specifically addresses the significant case, where propulsion is generated by the oscillation of a mass located in an internal cavity of the body. We provide a rigorous proof of the necessary and sufficient conditions for propulsion at the second order of magnitude of the force. These conditions are implemented and confirmed by numerical tests for bodies without fore-and-aft symmetry, while they are silent for bodies with such symmetry, like round ellipsoids. Consequently, in this case, propulsion can only occur at an order higher than the second. This problem is investigated by numerically integrating the entire set of equations, and the result shows that, in fact, propulsion does occur, thus opening new avenues for further analytical studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_20982 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the Propulsion of a Rigid Body in a Viscous Liquid by Time-Periodic Force with a Zero Average Edelmann, Joris Galdi, Giovanni P. Karakouzian, Mher M. Richter, Thomas Analysis of PDEs Fluid Dynamics We perform analytical and numerical analyses of the propulsion of a rigid body in a viscous fluid subjected to a periodic force with zero average over a period. This general formulation specifically addresses the significant case, where propulsion is generated by the oscillation of a mass located in an internal cavity of the body. We provide a rigorous proof of the necessary and sufficient conditions for propulsion at the second order of magnitude of the force. These conditions are implemented and confirmed by numerical tests for bodies without fore-and-aft symmetry, while they are silent for bodies with such symmetry, like round ellipsoids. Consequently, in this case, propulsion can only occur at an order higher than the second. This problem is investigated by numerically integrating the entire set of equations, and the result shows that, in fact, propulsion does occur, thus opening new avenues for further analytical studies. |
| title | On the Propulsion of a Rigid Body in a Viscous Liquid by Time-Periodic Force with a Zero Average |
| topic | Analysis of PDEs Fluid Dynamics |
| url | https://arxiv.org/abs/2510.20982 |