Journal of Fluid Mechanics

Papers

Time-dependent linear water-wave scattering in two dimensions by a generalized eigenfunction expansion

MICHAEL H. MEYLANa1 c1

a1 Department of Mathematics, The University of Auckland, New Zealand

Abstract

We consider the solution in the time domain of the two-dimensional water-wave scattering by fixed bodies, which may or may not intersect with the free surface. We show how the problem with arbitrary initial conditions can be found from the single-frequency solutions using a generalized eigenfunction expansion, required because the operator has a continuous spectrum. From this expansion we derive simple formulas for the evolution in time of the initial surface conditions, and we present some examples of numerical calculations.

(Received December 17 2008)

(Revised March 21 2009)

Key words

  • Wave-structure interactions;
  • Wave scattering

Correspondence:

c1 Email address for correspondence: meylan@math.auckland.ac.nz

Metrics