Asymptotic behavior of trapped modes in two-layer fluids

We investigate the trapping of oblique water-waves by horizontal cylinders in a two-layer liquid. Two cases depending on a small parameter are studied: first, the liquid densities are close to each other, and second, the density of the upper layer is small in comparison with that of the lower layer. We give sufficient conditions for wave trapping for appropriate limit problems. The main results involve asymptotic formulas for the surface and interfacial trapped mode frequencies. In addition, we prove comparison principles and sufficient conditions for the existence of trapped modes in various situations.

► We study the relation of trapped modes and the density ratio of two liquid layers. ► We give sufficient conditions for trapped modes for various geometries and liquid densities. ► Comparison principles for related geometric situations are found. ► Mathematically rigorous study based on spectral theory.