Influence of liquid viscosity on the three-dimensional sloshing in a square-base tank under longitudinal harmonic excitation

This study investigated the influence of liquid viscosity on sloshing characteristics in a square-base tank. Under horizontal harmonic excitation, hundreds of sloshing tests were performed with four oils of markedly different viscosities, while high-definition cameras simultaneously recorded the free-surface morphology and wave height. The experiments revealed four distinct sloshing patterns: planar standing waves, diagonal standing waves, swirling waves, and chaotic waves. These phenomena can be explained by the asymptotic multimodal theory of fluid dynamics. Specifically, low-viscosity liquids excite various wave modes—including planar, diagonal, swirling, and chaotic—at medium to high amplitudes and frequencies, and are highly sensitive to excitation conditions. With increasing viscosity, the frequency range of planar standing waves expands markedly, and diagonal standing waves emerge within a specific range of excitation amplitudes. In contrast, the frequency ranges of swirling and chaotic waves progressively shrink. For the highest-viscosity oil, all three-dimensional waveforms were suppressed, leaving only planar standing waves. This study is the first to experimentally demonstrate the significant influence of liquid viscosity on the sloshing behavior of a square-base tank. It provides an experimental basis and reference for elucidating sloshing mechanisms in liquid tanks and for the anti-sloshing design of ocean engineering structures.