A twin wavemaker model for liquid sloshing in a rectangular tank

Abstract

Sloshing of a liquid in a rectangular container under horizontal excitations is modelled using a wave basin analogue within the framework of a potential flow theory. An initial boundary-value problem is formulated replacing fixed walls of the tank with two orthogonal twin piston-type wavemaker paddle pairs. The proposed equivalent mechanical system may be applied to a class of problems covering irrotational flow of an inviscid and incompressible fluid inside partially-filled rectangular containers exposed to translatory oscillations. An analytical solution to the problem is provided under the assumption of a small-amplitude monochromatic forcing for a classical linear wavemaker in a closed flume and two- and three-dimensional twin wavemaker problems. The model is extended to cover an arbitrary horizontal motion using a semi-analytical approach based on a difference time-marching schemes applied to linearised evolution equations in a spectral domain. This relatively simple conceptual model may be used to design a novel experimental framework for studying water wave mechanics at smaller scales relying on elongated sloshing tanks substituting typical wave flumes.