In the present study, hundreds of experiments have been conducted on the three-dimensional free-surface and interfacial sloshing in a vertical cylindrical tank containing two immiscible liquids. The bounds of different free-surface and interfacial wave regimes are determined by maintaining fixed excitation amplitude and slowly increasing excitation frequency until another type of wave regime began to appear. In general, three types of the free-surface wave regimes are observed when the excitation frequency is in the neighborhood of the lowest natural frequency of the free surface, i.e., planar gravity wave, chaotic gravity wave, and swirling gravity wave. Similarly, when the excitation frequency is near the lowest natural frequency of the internal interface, three types of interfacial wave regimes, i.e., planar gravity wave, chaotic gravity-capillary wave, and swirling gravity-capillary wave, are generated. Besides, it is worth pointing out that when the excitation frequency is near the lowest natural frequency of the internal interface as well as very close to a third of the lowest natural frequency of the free surface, large-amplitude rotating wave motion occurs at both the free surface and the internal interface. This is due to even though the excitation frequency is far away from the natural frequency of the free surface, the secondary resonance can still become dominant and lead to large-amplitude motion of the free-surface rotating wave and subsequently influences the internal interface. This paper reveals that the sloshing behaviors of two-layer liquid in the vertical cylindrical tank are much more complicated than those of single-layer liquid.

Laboratory experiments were conducted to study primary and secondary resonant sloshing in a laterally excited rectangular container containing two-layer stratified liquids. The findings revealed that primary resonance of the free surface or the separation surface occurs when the forcing frequency closely matches the corresponding natural frequency. Some intriguing phenomena, such as the sudden wave amplitude increase and the downward shift in resonant peaks, can be observed due to the soft-spring effect. Secondary resonance arises when superharmonic or sub-harmonic frequencies associated with liquid sloshing closely align with the natural frequencies of the system. For the free surface, the secondary resonances of the first five modes occur at forcing frequencies closely related to a third of the first mode, half of the second mode, a third of the third mode, a quarter of the fourth mode, and a fifth of the fifth mode natural frequency of the free surface, respectively. Furthermore, secondary resonance can also manifest under other forcing conditions, such as when the harmonic at a fractional multiple is near the second mode natural frequency of the free surface. Regarding the separation surface, it is worth noting that secondary resonance occurs due to the dominant contribution of fractional harmonics of the forcing frequency. To the best of the authors' knowledge, this is the first systematic investigation of primary and secondary resonance behaviors in a two-layer liquid system.

The effect of ring baffles on suppressing the three-dimensional (3D) resonant sloshing in an upright cylindrical container is experimentally investigated. The main objectives of this work are to examine the effectiveness of various baffle configurations, to establish the stability boundaries of the stable steady-state waves in the unbaffled and baffled containers, to provide accurate experimental data for the verification of the analytical and numerical models, and to prompt future investigations. For this purpose, hundreds of sloshing experiments are conducted in a cylindrical container with or without a ring baffle. An analytical potential-flow solution and an asymptotic multimodal method are used to elucidate the experimental results. It is found that the vertical location of the ring baffle has small influence on the fundamental natural frequency of the system; however, it has a significant influence on the viscous damping and the damping rate increases gradually with the ascension of the baffle. When the distance between the baffle and the free liquid surface is sufficiently large, the system exhibits three types of resonant wave patterns, namely stable planar, stable swirling, and irregular chaotic. These wave patterns are qualitatively and quantitatively similar to those in the unbaffled container. When the baffle is near the free liquid surface, neither the chaotic waves nor the swirling waves take place, but a new wave pattern with the characteristic of multiple wave crests is observed. Probably, this is the first time that the 3D resonant sloshing in the baffled cylindrical container has been systematically investigated.