Water wave interactions with surface-piercing vertical barriers in a rectangular tank: Connections with Bloch waves and quasimodes

Abstract

Eigenmodes are studied for a fluid-filled rectangular tank containing one or more vertical barriers, and on which either Dirichlet or Neumann boundary conditions are prescribed on the lateral walls. In the case where the tank contains a single barrier, the geometry of the tank is equivalent to the unit cell of the cognate periodic array, and its eigenmodes are equivalent to standing Bloch waves. As the submergence depth of the barrier increases, it is shown that the passbands (i.e. frequency intervals in which the periodic array supports Bloch waves) become thinner, and that this effect becomes stronger at higher frequencies. The eigenmodes of a uniform array of vertical barriers in a rectan..