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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.
Liu et al. (Sun,) studied this question.