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A model of flow passing through the glottis is presented, that assumes a boundary layer. The fluid dynamic theory implies that a thin boundary layer formed in the vicinity of the glottal wall characterizes the flow behavior, including the flow separation, jet formation, and pressure loss across the channel. To analyze the boundary layer accurately, methods have been developed for solving the integral momentum relation on the basis of the similarity of the velocity profiles inside the layer, by assuming that the core flow velocity is known. On the other hand, development of the boundary layer reduces the effective size of the channel and increases the core flow velocity, thus causing the problem of viscous-inviscid interaction of the boundary layer. In this paper, the interactive boundary-layer problem is solved for glottal flow, and numerical results are compared with a conventional noninteractive model. In addition, the effects of the Reynolds number and glottal configuration on the flow behavior have been examined to validate the usefulness of the proposed flow analysis method.

A measurement principle of the three-dimensional electromagnetic articulographic device is presented. The state of the miniature receiver coil is described by five variables representing the position in the three-dimensional coordinate system and the rotation angles relative to it. When the receiver coil is placed in the magnetic field produced from the distributed transmitter coils, its state can be optimally estimated by minimizing the difference between the measured strength of the received signal and the predicted one using the known spatial pattern of the magnetic field. Therefore, the design and calibration of the field function inherently determine the accuracy in estimating the state of the receiver coil. The field function in our method is expressed in the form of a multivariate B spline as a function of position in the three-dimensional space. Because of the piecewise property of the basis function and the freedom in the selection of the rank and the number of basis functions, the spline field function has a superior ability to flexibly and accurately represent the actual magnetic field. Given a set of calibration data, the spline function is designed to form a smooth curved surface interpolating all of these data samples. Then, an iterative procedure is employed to solve the nonlinear estimation problem of the receiver state variables. Because the spline basis function is a polynomial, it is also shown that the calculation of the Jacobian or Hessian required to obtain updated quantities for the state variables can be efficiently performed. Finally, experimental results reveal that the measurement accuracy is about 0.2 mm for a preliminary condition, indicating that the method can achieve the degree of precision required for observing articulatory movements in a three-dimensional space. It is also experimentally shown that the Marquardt method is a better nonlinear programming technique than the Gauss-Newton or Newton-Raphson method for solving the receiver state problem.

The behavior of glottal flow can, to a large extent, be characterized by development and separation of the boundary layer. The point of flow separation is known to vary during the phonatory cycle due to change in channel configuration. To take the movable nature of the separation point into account, the boundary-layer equation is solved numerically, and the values of the characteristic quantities are determined as well as the point of separation. Development of the boundary layer in general reduces the effective size of the channel, and, therefore, increases the core flow velocity, which, in turn provides the boundary condition of the boundary-layer equation. The interaction between the viscous (boundary layer) and inviscid (core flow) parts of the glottal flow is, therefore, strongly indicated. To apply this viscous-inviscid interaction, the expression of the core flow is derived for a two-dimensional flow field, and is solved jointly with the boundary-layer equation. Numerical results are shown to examine the effect of the Reynolds number and glottal configuration, with special emphasis on the comparison of flow models developed for one- and two-dimensional flow fields. Numerical results are also quantitatively compared with data obtained from flow measurement experiments.