MODAL MODELLING OF THE NONLINEAR RESONANT FLUID SLOSHING IN A RECTANGULAR TANK II: SECONDARY RESONANCE

Abstract

In Part I of this work [Math. Mod. Meth. Appl. Sci.15 (2005) 1431–1458], we studied periodic (steady-state) solutions of an asymptotic nonlinear modal system which describes two-dimensional resonant sloshing in a rectangular tank. The system was derived by Faltinsen et al. (2000) under the assumption that the primary excited (lowest) natural mode gives the largest contribution to the wave patterns. We found that this assumption is not true in a certain frequency domain due to internal (secondary) resonance leading to an amplification of the second mode. This frequency domain can also be identified for the critical depth-to-breath ratio h = 0.3368 … which was discussed in Part I. In Part II, this secondary resonance is modelled by a double-dominant modal system by Faltinsen and Timokha (2001). A comparative analysis with the results from Part I is presented. The emphasis is placed on the case of the mentioned critical ratio when a double turning point arises in the branching diagram. The appearance of the double turning point explains why classical laboratory experiments by Fultz (1962) underestimate the value of the critical depth.