A Variational Characterization of Fluid Sloshing with Surface Tension
| Autor: | Tan, Chee Han, Hohenegger, Christel, Osting, Braxton |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | SIAM Journal of Applied Mathematics 77(3), p.995-1019 (2017) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1137/16M1104330 |
| Popis: | We consider the sloshing problem for an incompressible, inviscid, irrotational fluid in an open container, including effects due to surface tension on the free surface. We restrict ourselves to a constant contact angle and seek time-harmonic solutions of the linearized problem, which describes the time-evolution of the fluid due to a small initial disturbance of the surface at rest. As opposed to the zero surface tension case, where the problem reduces to a partial differential equation for the velocity potential, we obtain a coupled system for the velocity potential and the free surface displacement. We derive a new variational formulation of the coupled problem and establish the existence of solutions using the direct method from the calculus of variations. We prove a domain monotonicity result for the fundamental sloshing eigenvalue. In the limit of zero surface tension, we recover the variational formulation of the mixed Steklov-Neumann eigenvalue problem and give the first-order perturbation formula for a simple eigenvalue. Comment: 26 pages, 1 figure |
| Databáze: | arXiv |
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