Trapped modes and resonances for thin horizontal cylinders in a two-layer fluid

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