The undercutting of toneholes has been practised for centuries with the aim of improving the tuning and playability of woodwind instruments. The influence of undercutting on tuning can be understood in terms of linear acoustic theory. Its effect on other playing characteristics is thought to lie in its reduction of local non-linear flow phenomena (boundary layer separation and the formation of jets and vortices) at the tonehole. Particle Image Velocimetry (PIV) is used to examine the oscillating airflow around a model woodwind tonehole. Velocity and vorticity information is obtained and compared for a square-edged tonehole and an undercut tonehole at a variety of sound levels. The upstream, internal edge of the tonehole is found to be the location of the most significant local non-linear flow behaviour. Undercutting is found to reduce the strength of local non-linear flow phenomena at a given sound level. Microphone measurements carried out in a reverberation chamber show that undercutting the tonehole also reduces the harmonic distortion introduced to the radiated pressure signal by the non-linear flow. Proper Orthogonal Decomposition (POD) is then applied to PIV data of oscillating flow at the end of a tube. It is used to approximately separate the acoustic field from the induced local non-linear flow phenomena. The POD results are then used to approximate the percentage of kinetic energy present in the non-linear flow. POD analysis is applied to the case of flow around the two toneholes. It shows a smaller transfer of kinetic energy to non-linear flow effects around the undercut tonehole at a given sound level. The dependence of the local non-linear flow kinetic energy on Strouhal number is considered.