In the present paper, the sloshing flow in a cuboid tank forced to oscillate horizontally is investigated with both experimental and numerical approaches. The filling depth chosen is $h/L=0.35$ (with h the water depth and L the tank height), which is close to the critical depth. According to Tadjbakhsh & Keller (J. Fluid Mech., vol. 8, issue 3, 1960, pp. 442–451), as the depth passes through this critical value the response of the resonant sloshing dynamics changes from ‘hard spring’ to ‘soft spring’. The experimental tank has a thickness of $0.1L$ , reducing three-dimensional effects. High-resolution digital camera and capacitance wave probes are used for time recording of the surface elevation. By varying the oscillation period and the amplitude of the motion imposed on the tank, different scenarios are identified in terms of free-surface evolution. Periodic and quasi-periodic regimes are found in most of the frequencies analysed but, among these, sub-harmonic regimes are also identified. Chaotic energetic regimes are found with motions of greater amplitude. Typical tools of dynamical systems, such as Fourier spectra and phase maps, are used for the regime identification, while the Hilbert–Huang transform is used for further insight into doubling-frequency and tripling-period bifurcations. For the numerical investigation, an advanced and well-established smoothed particle hydrodynamics method is used to aid the understanding of the physical phenomena involved and to extend the range of frequencies investigated experimentally.

中文翻译：

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临界填充深度附近晃动流的不同情况

在本文中，通过实验和数值方法研究了被迫水平振荡的长方体储罐中的晃动流。所选择的填充深度为 $h/L=0.35$ （和H水深和L罐高度），接近临界深度。根据 Tadjbakhsh 和 Keller 的说法（J.流体机械。，卷。 8，第 3 期，1960 年，第 442–451 页），当深度超过此临界值时，共振晃动动力学的响应从“硬弹簧”变为“软弹簧”。实验槽的厚度为 $0.1升$ ，减少三维效应。高分辨率数码相机和电容波探头用于表面高程的时间记录。通过改变施加在罐上的振动周期和运动幅度，可以根据自由表面演化来识别不同的情况。在大多数分析的频率中都发现了周期性和准周期状态，但其中也确定了次谐波状态。混沌能量状态具有更大幅度的运动。动态系统的典型工具，例如傅里叶谱和相位图，用于状态识别，而希尔伯特-黄变换用于进一步了解倍频和三倍周期分岔。对于数值研究，使用先进且完善的平滑粒子流体动力学方法来帮助理解所涉及的物理现象并扩展实验研究的频率范围。