Nonlinearities in the dynamics of reciprocating pipe flow in relation tooscillating water column wave-energy converters

As a canonical type of wave energy converter, oscillating water column (OWC) devices have been employed in maritime engineering since the 19th century. In principle, these devices require no moving parts in the water and are thus reliable when exposed to the elements in the real-world. Theoretically, their behaviour is akin to that of reciprocating pipe flow (RPF), in a sense that both OWC and RPF can be described by a same ordinary differential equation (ODE). Like all wave energy converters, OWCs are designed to resonate, and their basic geometry is engineered to resonate using the predictions of linear theory. However, resonance implies large amplitudes, and working OWCs do exhibit large amplitudes that render the behaviour nonlinear, requiring the ODE to be nonlinear, too. In this work, we show that although the nonlinear terms can sometimes only affect the behaviour of RPFs/OWCs quantitatively, these terms can change the behaviour of the oscillations qualitatively in some cases, giving rise to nonlinear behaviour such as hysteresis due to bi-stability. To simplify the discussion, in this work, we consider thin-walled, cylindrical-shaped RPF/OWC devices, although some findings here can be extended to devices of other shapes. When appropriate, the results are related to design aspects of OWCs, specifically whether the nonlinearities can be harnessed for optimisation and control of OWCs.