Aerodynamics in two-dimensional vocal tract models

Abstract

A numerically tractable formulation of the Navier-Stokes equations, suitable for studying fluid flow in the vocal tract during speech production and for doing more natural speech synthesis, is described. These qualities are obtained by restricting consideration to two-dimensional vocal tract geometries and by introducing a velocity stream function A (ψ,θ) and a velocity potential Ω (ψ,θ). Here, (ψ,θ,φ) are curvilinear coordinates with φ being ignorable. Taking the divergence and curl of the momentum equation isolates the compressible wave motion in the velocity potential and the background “quasi-steady-state” flow in the stream function. This analytic separation of the two flow components allows for dramatic improvements in the accuracy and efficiency of any numerical simulation as compared to those obtained by directly integrating the primative equations. Full steady-state flow is represented compactly by a “momentum density stream function” Φ (ψ,θ). For invisid flow, a second-order elliptic PDE for Φ is obtained with the fluid density given self-consistently by Bernoulli's law. With viscosity, a higher-order equation for Φ results. Details of the formulation, geometry, and boundary conditions are presented.