标题： 近圆周流动处的风与水波相互作用 显示英文标题

标题： Interactions between Wind and Water Waves near Circular Flows

摘要： 本文涉及风与水波之间的动力学相互作用，这些相互作用通过欧拉方程的两相自由界面问题来表征。 我们提供了对一般两相流动线性化问题的全面推导。 然后，我们研究了围绕圆形稳态解的扰动波的不稳定性问题，并展示了不稳定模态可能位置的半圆结果。 我们还提出了在泰勒-库埃特流动附近风扰动水波不稳定的必要条件和充分条件。 显示英文摘要

摘要： This manuscript concerns the dynamical interactions between wind and water waves, which are characterized through two-phase free interface problems for the Euler equations. We provide a comprehensive derivation on the linearized problems of general two-phase flows. Then, we study the instability issues of perturbing waves around circular steady solutions, and we demonstrate a semi-circle result on the possible locations of unstable modes. We also present necessary conditions and sufficient ones for the instability of wind-perturbing water waves near Taylor-Couette flows.