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 rectangular tank are also considered. They are found to be a superposition of left- and right-propagating Bloch waves, which couple together at the lateral walls of the tank. A homotopy procedure is used to relate the eigenmodes to the quasimodes of the same uniform array in a fluid of infinite horizontal extent, and the quasimodes are shown to govern the response of the array to incident waves. Qualitative features of the mode shapes are typically preserved by the homotopy, which suggests that the resonant responses of the array in an infinite fluid can be understood in terms of modes of the array in a finite tank.
• The modes of a fluid-filled rectangular tank containing one or more vertical barriers are explored.
• The modes of the single barrier tank are equivalent to standing Bloch waves of the cognate periodic array, and thus, their resonant frequencies delineate the edges of the passbands.
• As the barrier submergence increases, pairs of these resonant frequencies move closer together, which pinches the passbands—an effect which becomes stronger at higher frequencies.
• The modes of the multiple barrier tank consist of a superposition of forwards and backwards propagating Bloch waves.
• A homotopy procedure to relate the resonances of the multiple barrier tank to the quasimodes of the same array in a fluid of infinite horizontal extent, and therefore to the resonant response to plane wave forcing.