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Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. (English) Zbl 0990.76006
The paper describes an intensive irrotational motion (sloshing) of incompressible fluid partially occupying a tank performing arbitrary three-dimensional motion. The general form of the corresponding discrete infinite-dimensional modal system is derived by using the Bateman-Luke (pressure-integral Lagrangian) variational principle. The free surface motion and velocity potential are expanded in generalized Fourier series, and the general multidimensional structure of equations is approximated to analyse the sloshing in a rectangular tank with finite water depth. The tank oscillates arbitrarily with small amplitude and with an average frequency close to the lowest natural frequency of the fluid motion. The theory is validated by experimental results. It is shown that transients and associated nonlinear beating are important. The theory is invalid when either the water depth is small or water impacts heavily on the tank ceiling. Alternative expressions for hydrodynamic loads are presented which can facilitate the simulations of coupled vehicle-fluid systems.

MSC:
76B10Jets and cavities, cavitation, free-streamline theory, water-entry problems, etc.
76B07Free-surface potential flows
76M30Variational methods (fluid mechanics)