Simulation studies of the flute

Simulations of the transverse flute using direct numerical solutions of the Navier-Stokes equations are described. Constructing a numerical model of the instrument itself is straightforward, but making a semi-realistic model of the player's lips is more challenging. One solution to this problem is described and used to explore the kinds of tones that are possible. Conditions are found for which the model produces a well-behaved musical tone for a range of blowing speeds. When the blowing speed is increased beyond this range the behavior becomes complex and is appears to be chaotic. An analysis of this behavior in terms of the sensitivity to initial conditions and a route to chaos involving Hopf bifurcations is described. The relevance of these results to real instruments played by real players is also discussed. [Research supported by NSF grant PHY1513273.]