Direct numerical solutions of the Navier-Stokes equations have been used to model the recorder, trumpet, and clarinet. This first-principles approach to calculating the air flow through a wind instrument allows the investigation of a number issues that are difficult or impossible to address with more approximate modeling. The power of this kind of model is illustrated in studies of (1) how the labium position in a recorder affects the tonal properties, (2) qualitative failure of the Bernoulli equation in calculations of the pressure near the lips of a trumpet player, and (3) the dynamics of a clarinet reed. Work supported by NSF grant PHY1513273.
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