Oscillating flow past a streamwise periodic array of cylinders

As a simple two-dimensional model to investigate effects of nerve roots on the flow and transport in the spinal canal, we consider the flow induced by the interaction of a periodically oscillating stream and an infinite array of equally spaced identical cylinders aligned with the unperturbed flow. Specific attention is given to flows involving small values of the ratio e of the stroke length to the cylinder radius, when the time-averaged Lagrangian motion can be described as the sum of a steady-streaming component and a Stokes-drift component, which are determined for selected values of the relevant Womersley number. Also, consideration is given to configurations with order-unity values of e and inharmonic velocity oscillations. Numerical integrations are used to characterize the resulting flow for different values of the inter-cylinder distance.