Stability of periodic arrays of cylinders across the stream by direct simulation

Abstract

We treat the problem of the stability of an infinite horizontal array of cylinders, spaced periodically, by a direct numerical simulation of the Navier–Stokes equations for steady flow at Reynolds numbers less than or equal to 100. We find that the only stable configuration for the array is one with equal spacing between cylinders and all cylinders lying on a line perpendicular to the flow. The array is found to be stable under displacements of the cylinders perpendicular and parallel to the array. We say a perturbation is stable when it gives rise to a force which acts to restore the original stable configuration. Our results are consistent with experiments in which spheres were confined by the sidewalls of a fluidized bed to move in two dimensions. As a secondary issue we consider the variation with parameters of the length and width of wakes behind cylinders.