Acoustic streaming resulting from the time-harmonic compression of the cochlear capsule is examined in this paper. The cochlear pressure is expressed as an integral equation in the cochlear partition velocity. Rapid spatial variation in the velocity of the cochlear partition requires one to treat high-order fluid modes within the cochlear fluid. Hence, evanescent pressure modes are needed in the analysis. Asymmetry in the oval and the round window velocity is shown to give rise to a pressure gradient across the cochlear partition. The time-average fluid motion is obtained using the method of matched asymptotic expansions in conjunction with numerical evaluation of the outer flow field.

1.
Allen
,
J. B.
(
1977
). “
Two-dimensional cochlear fluid model: New results
,”
J. Acoust. Soc. Am.
61
,
110
119
.
2.
Andrade
,
E. N.
(
1931
). “
On the circulation caused by the vibration of air in a tube
,”
Proc. R. Soc. Lond.
134
,
445
470
.
3.
Bárány
,
E.
(
1938
). “
A contribution to the physiology of bone conduction
,”
Acta Oto-Laryngol. Suppl.
26
,
1
223
.
4.
Chhan
,
D.
, and
Thompson
,
C.
(
2010
). “
Application of matched asymptotic expansions to the analysis of compressive bone conduction
,”
J. Acoust. Soc. Am.
127
,
1987
.
5.
Eckert
,
C.
(
1948
). “
Vortices and streams caused by sound waves
,”
Phys. Rev.
73
,
68
76
.
6.
Faraday
,
M.
(
1831
). “
On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces
,”
Philos. Trans. R. Soc. B.
121
,
299
340
.
7.
Gerstenberger
,
C.
, and
Wolter
,
F.-E.
(
2013
). “
Numerical simulation of acoustic streaming within the cochlea
,”
J. Comput. Acoust.
21
,
1350019
.
8.
Herzog
,
H.
, and
Krainz
,
W.
(
1926
). “
“Das knochenleitungsproblem. Theoretische erwagungen” (“The conduction problem. Theoretical considerations”)
,”
Z. Hals Nasen Ohrenheilk
15
,
300
313
.
9.
Ho
,
M.-L.
(
2019
). “
Third window lesions
,”
Neuroimaging Clin. N. Am.
29
,
57
92
.
10.
Lesser
,
M. B.
, and
Berkley
,
D. A.
(
1972
). “
Fluid mechanics of the cochlea.
Part 1
,”
J. Fluid Mech.
51
,
497
512
.
11.
Lighthill
,
M. J.
(
1992
). “
Acoustic streaming in the ear itself
,”
J. Fluid Mech.
239
,
551
606
.
12.
Neely
,
S. T.
(
1981
). “
Finite difference solution of a two dimensional mathematical model of the cochlea
,”
J. Acoust. Soc. Am.
69
,
1386
1393
.
13.
Nyborg
,
W. L.
(
1953
). “
Acoustic streaming near due to attenuated plane waves
,”
J. Acoust. Soc. Am.
25
,
68
75
.
14.
Nyborg
,
W. L.
(
1958
). “
Acoustic streaming near a boundary
,”
J. Acoust. Soc. Am.
30
,
329
338
.
15.
Rayleigh
,
L.
(
1883
). “
On the circulation of air observed in kundt's tube, and on some allied acoustic problem
,”
Philos. Trans. R. Soc. B.
175
,
1
21
.
16.
Patankar
,
S. V.
, and
Spalding
,
D. B.
(
1972
). “
A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows
,”
Int. J. Heat Mass Transf.
15
,
1787
1806
.
17.
Scott
,
M. R.
, and
Watts
,
H. A.
(
1977
). “
Computational solution of linear two-point boundary value problem via orthonormalization
,”
SIAM J. Numer. Anal.
14
,
40
70
.
18.
Sondhi
,
M. M.
(
1978
). “
Method for computing motion in a two-dimensional cochlear model
,”
J. Acoust. Soc. Am.
63
,
1468
1477
.
19.
Stenfelt
,
S.
,
Hato
,
N.
, and
Goode
,
R. L.
(
2004
). “
Fluid volume displacement at the oval and round windows with air and bone conduction stimulation
,”
J. Acoust. Soc. Am.
115
,
797
812
.
20.
Sumner
,
L.
,
Mestel
,
J.
, and
Reichenbach
,
T.
(
2021
). “
Steady streaming as a method for drug delivery to the inner ear
,”
Sci. Rep.
11
,
57
.
21.
Thompson
,
C.
(
1984
). “
Acoustic streaming in a waveguide with slowly varying height
,”
J. Acoust. Soc. Am.
75
,
97
107
.
22.
Tonndorf
,
J.
(
1962
). “
Compressional bone conduction in cochlear models
,”
J. Acoust. Soc. Am.
34
,
1127
1131
.
23.
Tonndorf
,
J.
(
1966
). “
Bone conduction Studies in experimental animals
,”
Acta Oto-Laryngol. Suppl.
1
132
.
24.
Tonndorf
,
J.
(
1970
). “
Nonlinearities in cochlear hydrodynamics
,”
J. Acoust. Soc. Am.
47
,
579
591
.
25.
v. Békésy
,
G.
(
1932
). “
Zur theorie des hörens bei der schallaufnahme durch knochenleitung” (“On the theory of hearing when recording sound through bone conduction”)
,”
Ann. Phys.
405
(
1
),
111
136
.
26.
v. Békésy
,
G.
(
1948
). “
Vibration of the head in a sound field and its role in hearing bone conduction
,”
J. Acoust. Soc. Am.
20
,
749
760
.
27.
v. Békésy
,
G.
, “
Concerning pleasures observing, mechanics inner ear
,” in
Nobel Lectures, Physiology or Medicine
(
Elsevier Publishing
,
Amsterdam
,
1964
). pp.
1942
1962
.
28.
Watts
,
L.
(
2000
). “
The mode-coupling
Liouville-Green approximation for a two-dimensional cochlear model
,”
J. Acoust. Soc. Am.
108
,
2266
2271
.
29.
Zwislocki
,
J.
(
1953
). “
Wave motion in the cochlea caused by bone conduction
,”
J. Acoust. Soc. Am.
25
,
986
989
.
You do not currently have access to this content.