Abstract

Co-author: Feng Xu (University of Nottingham)

Large-amplitude self-excited oscillations of high-Reynolds-number flow in a long flexible-walled channel can exhibit vigorous slamming motion, whereby the channel is almost completely occluded over a very short interval in space and time. Treating the flexible channel wall as an inertialess elastic membrane, this near-singular behaviour is exhibited in two-dimensional Navier-Stokes simulations and can be captured in a reduced one-dimensional PDE model (Stewart et al. J. Fluid Mech. 662:288, 2010). The properties of the rigid parts of the system, upstream and downstream of the membrane, play a major role in determining the onset of oscillations. In order to investigate the extreme flow structure that arises during a brief slamming event, we systematically reduce the PDE model to a third-order nonlinear algebraic-differential system, which identifies the likely dominant physical balances.