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Cochlea is an important auditory organ in the inner ear. In most mammals, itis coiled as a spiral. Whether this specific shape influences hearing is stillan open problem. By employing a three dimensional fluid model of the cochleawith an idealized geometry, the influence of the spiral geometry of the cochleais examined. We obtain solutions of the model through a conformaltransformation in a long-wave approximation. Our results show that the netpressure acting on the basilar membrane is not uniform along its spanwisedirection. Also, it is shown that the location of the maximum of the spanwisepressure difference in the axial direction has a mode dependence. In thesimplest pattern, the present result is consistent with the previous theorybased on the WKB-like approximation [D. Manoussaki, Phys. Rev. Lett. 96,088701(2006)]. In this mode, the pressure difference in the spanwise directionis a monotonic function of the distance from the apex and the normal velocityacross the channel width is zero. Thus in the lowest order approximation, wecan neglect the existance of the Reissner's membrane in the upper channel.However, higher responsive modes show different behavior and, thus, the realmaximum is expected to be located not exactly at the apex, but at a positiondetermined by the spiral geometry of the cochlea and the width of the cochlearduct. In these modes, the spanwise normal velocities are not zero. Thus, itindicates that one should take into account of the detailed geometry of thecochlear duct for a more quantitative result. The present result clearlydemonstrates that not only the spiral geometry, but also the geometry of thecochlear duct play decisive roles in distributing the wave energy.

Resultant pressure distribution pattern along the basilar membrane in the spiral shaped cochlea