Existence and some properties of waves trapped by submerged cylinders

Abstract

In this paper the mathematical formulation associated with waves trapped by submerged cylinders is recast as a standard eigenvalue problem. In this way the existence is proven of trapped waves for every frequency Ω, and for arbitrary geometry of the submerged cylinder. At the same time a simple expression for the first eigenvalue and eigenmode, correct in the limits Ω → 0 or Ω → ∞, is derived. The expression can be a useful approximation for a structure relatively transparent to the wave action such as, for instance, a semisubmersible platform.