A Function-theoretic approach to a two-dimensional transient wave-body interaction problem

Abstract

The linearized initial-boundary value problem describing the liquid motion in an ocean of infinite extent, caused by a two-dimensional floating body is investigted. Introducing a time-dependent complex velocity potential f (w,t) and performing an analytic continuation in the upper half plane, it is shown that the solution of the above problem can be expressed in terms of the solution of an initial-value problem for F(w,t). The latter problem is solved explicitly by means of an appropriately defined Laplace transform, acting on time-dependent ω-analytic functions. The simultaneous presence of the space complex variable and the trabsform complex variable ω=x₂+ix₃ and the transform complex variable p=δ+jω enforces us to work with a set of double complex numbers C_ij={k+λi+μj+vij, k,λ,μ,v∊R} and develop some elements of analytic function theory on this set. The possibility of applying this Laplace transform to other similar problems is also discussed.

Keywords:

• water waves
• series solutions
• expansion theorems
• transform methods
• Laplace transform
• nonlocal wave equations

AMS:

• 76B15
• 35C10
• 35A22
• 44A10