Vocal fold (VF) motion is a fundamental process in voice production, and is
also a challenging problem for direct numerical computation because the VF
dynamics depend on nonlinear coupling of air flow with the response of elastic
channels (VF), which undergo opening and closing, and induce internal flow
separation. A traditional modeling approach makes use of steady flow
approximation or Bernoulli's law which is known to be invalid during VF
opening. We present a new hydrodynamic semi-continuum system for VF motion. The
airflow is modeled by a quasi-one dimensional continuum aerodynamic system, and
the VF by a classical lumped two mass system. The reduced flow system contains
the Bernoulli's law as a special case, and is derivable from the two
dimensional compressible Navier-Stokes equations. Since we do not make steady
flow approximation, we are able to capture transients and rapid changes of
solutions, e.g. the double pressure peaks at opening and closing stages of VF
motion consistent with experimental data. We demonstrate numerically that our
system is robust, and models in-vivo VF oscillation more physically. It is also
much simpler than a full two-dimensional Navier-Stokes system.Comment: 27 pages,6 figure