AI 中文总结
该研究采用弗洛凯分析探究垂直振动圆柱中瑞利-泰勒与法拉第不稳定性的耦合机制，明确振动振幅、横向约束等因素对不稳定性模式的影响，揭示了受限多相流中界面不稳定性的复杂演化规律。
AI 中文摘要
界面不稳定性控制受限多相流中的混合过程，但驱动不稳定性的两种机制通常被独立研究：由压力梯度驱动的瑞利-泰勒（RT）不稳定性，会放大长波长模式；以及参数受迫的法拉第不稳定性，会选择更短波长的谐波或次谐波模式。当不利密度差与垂直振动共同作用时，两种机制会相互竞争，单独一种无法描述系统响应。我们采用弗洛凯（Floquet）分析表征垂直振动圆柱中法拉第-瑞利-泰勒（Faraday-RT）波的 onset、增长、模态结构及速度场，通过方位角波数、径向（贝塞尔）模式和弗洛凯谐波进行解析。该公式可还原经典RT和法拉第极限，并复现实验测得频率下的不稳定性 onset。对于自由滑动界面，增大振动振幅会使主导不稳定性机制从RT增长依次转变为次谐波、再转变为谐波法拉第响应。横向约束还可稳定单个RT模式，这在无界域中无法实现，尽管其他法拉第模式仍可能不稳定。固定接触线会耦合原本独立演化的径向模式，使不稳定模式成为RT不稳定分量与法拉第稳定分量的叠加，这种叠加改变了不稳定性机制，产生更丰富的径向图案。对不稳定模式的重构揭示了成像无法获取的（线性）速度场，证明了不稳定性如何更广泛地改变流动。
英文摘要
Interfacial instabilities govern the mixing in confined multiphase flows. Yet, the two mechanisms that drive them are usually studied independently: the pressure-gradient-driven Rayleigh--Taylor (RT) instability, which amplifies long-wavelength modes, and the parametrically forced Faraday instability, which selects shorter-wavelength harmonic or subharmonic modes. When an adverse density contrast and vertical vibration act together, the two compete, and neither alone describes the response. We use Floquet analysis to characterize the onset, growth, modal structure, and velocity fields of Faraday--RT waves in a vertically vibrated cylinder, resolved by azimuthal wavenumber, radial (Bessel) mode, and Floquet harmonic. The formulation recovers the classical RT and Faraday limits and reproduces the instability onset at the frequencies measured experimentally. For a free-sliding interface, increasing the vibration amplitude shifts the dominant instability mechanism from RT growth to subharmonic and then harmonic Faraday responses. Lateral confinement can also stabilize individual RT modes, which is not possible in an unbounded domain, although other Faraday modes may remain unstable. Pinning the contact line couples radial modes that otherwise evolve independently, allowing the unstable mode to be a superposition of RT-unstable and Faraday-stable components. This superposition alters the instability mechanism, producing a richer radial pattern. Reconstruction of the unstable modes shows the (linear) velocity fields that imaging cannot access and demonstrates how the instabilities can change the flow more broadly.
