  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.
