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Resonant three-dimensional nonlinear sloshing in a square-base basin. (English) Zbl 1053.76006
The adaptive third-order modal approach was modified to handle three-dimensional sloshing in a rectangular-base basin. The assumptions are incompressible fluid, irrotational flow, no overturning waves and no roof impact. The free surface should intersect the tank walls perpendicularly. In addition, the lateral and angular external forcing is sufficiently small and characterized by a dimensionless parameter ε1. The modal approach of the authors allows to derive an infinite-dimensional system of ordinary differential equations coupling nonlinearly time-dependent (modal) functions describing time-evolution of the corresponding natural surface modes.

MSC:
76B10Jets and cavities, cavitation, free-streamline theory, water-entry problems, etc.
76M45Asymptotic methods, singular perturbations (fluid mechanics)