Faltinsen, Odd M.; Rognebakke, Olav F.; Lukovsky, Ivan A.; Timokha, Alexander N. Multidimensional modal analysis of nonlinear sloshing in a rectangular tank with finite water depth. (English) Zbl 0990.76006 J. Fluid Mech. 407, 201-234 (2000). 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. Reviewer: Adrian Carabineanu (Bucureşti) Cited in 2 ReviewsCited in 70 Documents MSC: 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing 76B07 Free-surface potential flows for incompressible inviscid fluids 76M30 Variational methods applied to problems in fluid mechanics Keywords:variational principle; free surface motion; discrete infinite-dimensional modal system; irrotational motion; incompressible fluid; Bateman-Luke variational principle; velocity potential; Fourier series; rectangular tank; small amplitude; lowest natural frequency; nonlinear heating; hydrodynamic loads PDFBibTeX XMLCite \textit{O. M. Faltinsen} et al., J. Fluid Mech. 407, 201--234 (2000; Zbl 0990.76006) Full Text: DOI