Phase averaging of the velocity fields in an oscillating water column using splines

The principal objective of this paper is to present a phase averaging method by curve fitting using B-splines. The method was designed specifically to process phase-clumped and discontinuous periodic data. Phase averaging by ensemble averaging of data clumped in phase will cause phase bias error if the mean phase of the clumped data does not equal the desired phase. The curve-fitting method presented here avoids phase bias error. The performance of the curve-fitting method was compared favourably with the ensemble averaging method when processing phase-clumped experimental data. Generally, the curve-fitting method exceeded the performance of the ensemble averaging method when the data were clumped in phase and matched the performance of the ensemble averaging method when the data were randomly distributed in phase. Experimentally obtained phase-clumped two-dimensional velocity fields at the centre-line of a forward-facing bent-duct oscillating water column were processed using the curve-fitting method. The phase-averaged velocity fields were combined for visualization purposes in the form of animated graphics interchange format (GIF) images to show the velocity fields over a wave cycle. The GIF images correspond to the four separate monochromatic wave frequencies tested and accompany the online version of this paper. The GIF images reveal the two-dimensional phase-averaged flow characteristics at the centre-line of the model with phenomena including oscillating flow, water column heave and slosh, front-wall swash and down wash, an outflow jet and vortices. It was concluded that phase averaging using splines finds a niche for the phase averaging of data which are dispersed (or clumped) in phase.