Trapped modes in a two-layer fluid

Trapped-mode frequencies are computed for submerged horizontal circular cylinders in a two-layer fluid consisting of a finite layer bounded above by a free surface and below by an infinite layer of greater density. Two separate cases are examined. First we consider waves which propagate along the top of a single cylinder at frequencies below the cut-off for wave propagation away from the cylinder, and find modes where the motion is concentrated around the interface, modes which are concentrated around the free surface, and modes which involve significant motion of both the interface and the free surface. Secondly, we compute modes above the cut-off for a pair of submerged cylinders in the lower fluid.