On the adequacy of the Peterson-Bogert model and on the effects of viscosity in cochlear dynamics

Viergever, M. A., Kalker, J. J.


Journal of Engineering Mathematics 8 (2), p. 149-156


Based on a simplified model of the cochlea a one-dimensional approach (the Peterson-Bogert model) is compared with a three-dimensional one. The results appear to be in agreement provided the impedance of the partition is large. This is true for low frequencies except in the region of maximum membrane amplitude. For low frequencies, moreover, the fluid can be considered as incompressible. The influence of the viscosity is investigated by localizing the entire viscous force in a boundary layer. This layer is shown to occur in the fluid. Besides it is concluded that the rotation is approximately largest where the membrane has its maximum amplitude. This can be an explanation for the appearance of eddies at that point.