The Floquet theory is combined with the unsteady Orr–Sommerfeld equations for the first time to model the linear stability of a fluid mud–water interface under the influence of a linear long travelling wave (or linear shallow water wave). The modelling results reveal three instability modes that could appear on the fluid mud–water surface: the Kelvin–Helmholtz (K–H) and finite-wavelength (F-W) instabilities, which are also present in steady two-layer systems, and parametric instability, which is only seen in periodic problems. The growth rate of the parametric instability is generally small, but it affects the growth rate curves of the other two instabilities. The K–H and F-W instabilities are found to be dominant, and each plays an important role in determining the evolution of the fluid mud–water interface. Both the K–H and F-W instabilities grow with increasing water depth and decreasing wave period as well as with decreasing thickness and density of the mud layer. However, they exhibit distinct dependencies on the fluid mud-to-water viscosity ratio and compete near the critical conditions. For unstable flow near the critical conditions, the K–H instability dominates over the F-W instability at a low viscosity ratio and vice versa at a high viscosity ratio, while for unstable flow far beyond the critical conditions, the K–H instability is dominant regardless of the viscosity ratio. These results are practically instructive for waterway and harbour construction and protection since they provide valuable insights into the early dynamics of the instability mechanisms of the fluid mud–water interface.

Floquet理论首次与非定常的Orr-Sommerfeld方程组合，以模拟在线性长行波（或线性浅水波）影响下的泥浆-水界面的线性稳定性。建模结果显示出可能出现在流体泥水表面的三种不稳定性模式：开尔文-亥姆霍兹（KH）和有限波长（FW）不稳定性，它们也存在于稳定的两层系统中，以及参数不稳定性，这仅在周期性问题中可见。参数不稳定性的增长率通常很小，但会影响其他两个不稳定性的增长率曲线。发现K–H和FW不稳定性是主要因素，它们在确定流体泥浆—水界面的演化中都起着重要作用。K–H和FW的不稳定性都随着水深的增加和波浪周期的减小以及泥层厚度和密度的减小而增大。但是，它们对流体泥浆与水的粘度比表现出明显的依赖性，并且在临界条件附近竞争。对于临界条件附近的不稳定流动，在低粘度比下，K–H不稳定性占主导地位，而在高粘度比率下，F–W不稳定，反之亦然；而对于远远超过临界条件的不稳定流动，无论如何，K–H不稳定性都占主导地位。粘度比。这些结果对水路和港口的建设和保护具有实际指导意义，因为它们为流体泥浆-水界面失稳机理的早期动态提供了宝贵的见识。