Fluid mechanics of a recorder: coherent structures and sound generation*

The recorder is perhaps the simplest woodwind musical instrument, and despite its 700-year history, a complete description of the interplay between the hydrodynamic and sound generation processes in the labium is yet lacking. The aim of this work is to gain insight into these processes using simplified simulations and hydrodynamic stability theory. To this end, we consider a computational model of a recorder parametrized by its main geometric and flow features, and explore the parameter space using two-dimensional flow simulations based on immersed boundaries to determine the onset of coherent structures and their main statistical properties. Then, these structures and their sensitivity to changes in the geometry of the labium and flow parameters are analyzed, as well as their interaction with resonant acoustic modes in the chimney. Finally, the implication of these results to the design of these instruments and their playability will be discussed.