This paper addresses the viscous flow developing about an array of equally spaced identical circular cylinders aligned with an incompressible fluid stream whose velocity oscillates periodically in time. The focus of the analysis is on harmonically oscillating flows with stroke lengths that are comparable to or smaller than the cylinder radius, such that the flow remains two-dimensional, time-periodic and symmetric with respect to the centreline. Specific consideration is given to the limit of asymptotically small stroke lengths, in which the flow is harmonic at leading order, with the first-order corrections exhibiting a steady-streaming component, which is computed here along with the accompanying Stokes drift. As in the familiar case of oscillating flow over a single cylinder, for small stroke lengths, the associated time-averaged Lagrangian velocity field, given by the sum of the steady-streaming and Stokes-drift components, displays recirculating vortices, which are quantified for different values of the two relevant controlling parameters, namely, the Womersley number and the ratio of the inter-cylinder distance to the cylinder radius. Comparisons with results of direct numerical simulations indicate that the description of the Lagrangian mean flow for infinitesimally small values of the stroke length remains reasonably accurate even when the stroke length is comparable to the cylinder radius. The numerical integrations are also used to quantify the streamwise flow rate induced by the presence of the cylinder array in cases where the periodic surrounding motion is driven by an anharmonic pressure gradient, a problem of interest in connection with the oscillating flow of cerebrospinal fluid around the nerve roots located along the spinal canal.

The electrostatic force on a charge above a neutral conductor is generally attractive. Surprisingly, that force becomes repulsive in certain geometries (Levin & Johnson, Am. J. Phys., vol. 79, issue 8, 2011, pp. 843–849), a result that follows from an energy theorem in electrostatics. Based on the analogous minimum energy theorem of Kelvin (Camb. Dublin Math. J., vol. 4, 1849, pp. 107–112), valid in the theory of ideal fluids, we show corresponding effects on steady and unsteady fluid forces in the presence of boundaries. Two main results are presented regarding the unsteady force. First, the added mass is proven to always increase in the presence of boundaries. Second, in a model of a body approaching a boundary, where the unsteady force is typically repulsive (Lamb, Hydrodynamics, 1975, § 137, University Press), we present a geometry where the force can be attractive. As for the steady force, there is one main result: in a model of a Bernoulli suction gripper, for which the steady force is typically attractive, we show that the force becomes repulsive in some geometries. Both the unsteady and steady forces are shown to reverse sign when boundaries approximate flow streamlines, at energy minima predicted by Kelvin's theorem.

The collapse of a quasi-two-dimensional column of cohesive granular media is investigated experimentally and numerically in the framework of a continuum model. The configuration is an initial parallelepiped-shaped granular pile, which is suddenly released by opening a retaining door. The experiments rely on a model material developed by Gans et al. (Phys. Rev. E, vol. 101, 2020, 032904) made of silica particles coated with polyborosiloxane, for which the adhesive interparticle force can be tuned by controlling the thickness of the coating. Numerically, the collapse is simulated using a simple cohesive rheological model implemented in a two-dimensional Navier–Stokes solver. We investigate the role of cohesion on the stability of the column, the mode of failure, the flow dynamics and the geometry of the final deposit. Our results show that the continuum model captures the main features observed experimentally.