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## Journal of Fluid Mechanics

- Journal of Fluid Mechanics / Volume 239 / June 1992, pp 551- 606
- Copyright © 1992 Cambridge University Press
- DOI: http://dx.doi.org/10.1017/S0022112092004531 (About DOI), Published online: 26 April 2006

## Acoustic streaming in the ear itself
## AbstractJust as mean motions, usually described as acoustic streaming, can be generated by sound waves, so also those cochlear travelling waves into which incident sound waves are converted in the liquid-filled mammalian inner ear are capable of generating mean motions. These predominate, for acoustic components of each frequency ω, near the characteristic place where the wave energy Even though the nature of cochlear travelling waves, as determined (above all) by the sharply and continuously falling distribution of stiffness for the basilar membrane vibrating within the cochlear fluids, is very different from that of ordinary sound waves (see §§2, 3 and 4 respectively for energy distribution along the length of the cochlea, over a cochlear cross-section and within boundary layers), nevertheless a comprehensive analysis of mean streaming motions in the cochlea shows them to be governed by remarkably similar laws. The expression
\[
{\textstyle\frac{1}{4}}V^2c^{-1}-{\textstyle\frac{3}{4}}V({\rm d}V/{\rm d}x)\,\omega^{-1}
\]
(equation (1)) appropriate to a wave travelling in the Farther from the boundary layer attached to the basilar membrane, the mean streaming is derived (§9) as a low-Reynolds-number motion compatible with the distribution (1) of ‘effective slip velocity’ at the boundary. This velocity's precipitous fall to zero at the characteristic place is shown (§§9 and 10) to produce there a mean volume outflow
\[
q = \frac{0.15 E^{\max}}{\rho(\omega\nu)^{\frac{1}{2}}L}
\]
(equation (160)) per unit length of the basilar membrane into the scala media; here, ρ and ν are the endolymph's density and kinematic viscosity (essentially, those of water) and Equation (160), derived here for a freely propagating wave (and so not allowing for enhancements from any travelling-wave amplification – discussed qualitatively in §3 – due to forcing by vibrations of outer hair cells) is the main conclusion of this paper. Physiological questions of whether this flow |