Exact solutions of the linear water-wave problem describing oblique waves over a submerged horizontal cylinder of small (but otherwise fairly arbitrary) cross-section in a two-layer fluid are constructed in the form of convergent series in powers of the small parameter characterizing the “thinness” of the cylinder. The terms of these series are expressed through the solution of the exterior Neumann problem for the Laplace equation describing the flow of unbounded fluid past the cylinder. The solutions obtained describe trapped modes corresponding to discrete eigenvalues of the problem (lying close to the cut-off frequency of the continuous spectrum) and resonances lying close to the embedded cut-off. We present certain conditions for the submergence of the cylinder in the upper layer when these resonances convert into previously unobserved embedded trapped modes.

线性水波问题的精确解描述了两层流体中小（但在其他方面相当任意）横截面的水下水平圆柱体上的斜波，以小参数幂的收敛级数的形式构造圆柱体的“薄”。这些级数的项通过求解拉普拉斯方程的外部诺依曼问题来表示，该方程描述了通过圆柱体的无界流体的流动。获得的解决方案描述了对应于问题的离散特征值（接近连续谱的截止频率）的陷获模式和接近嵌入截止频率的共振。