The intensity coherence function of time for partially saturated acoustic propagation through internal waves is calculated with a method that is improved over previous treatments. Two specific improvements are introduced: the usual expansion in (1/ΛΦ2) is carried out to a higher order, and then the terms of that expansion are calculated with a new perturbative method. The method is applied to propagation without a sound channel, for both phase-screen and continuous-medium cases. The validity of the new perturbative method is estimated by calculating the next order error terms. Accuracies at the few-percent level are found. The new analytic formulas are also corroborated with numerical integration. Finally, the method is applied to a specific ocean-acoustic experiment [Azores Fixed Acoustic Range (AFAR)]. In order to achieve good agreement with experiment it will be necessary to add an accurate treatment of the sound channel to the present perturbation method.

Topics
Acoustical oceanography, Acoustic signal processing, Acoustic wave propagation, Perturbation theory, Numerical integration, Internal waves
1.
S. Flatté, R. Dashen, W. Munk, K. Watson, and F. Zachariasen, Sound Transmission through a Fluctuating Ocean (Cambridge University Press, Cambridge, 1979).
2.
S. M.
Flatté
, “
Wave propagation through random media: Contributions from ocean acoustics
,”
Proc. IEEE
71
,
1267
–
1294
(
1983
).
Google Scholar
Crossref
Search ADS
 
3.
S.
Flatté
,
S.
Reynolds
, and
R.
Dashen
, “
Path-integral treatment of intensity behavior for rays in a sound channel
,”
J. Acoust. Soc. Am.
82
,
967
–
972
(
1987
).
Google Scholar
Crossref
Search ADS
 
4.
S.
Flatté
,
S.
Reynolds
,
R.
Dashen
,
B.
Buehler
, and
P.
Maciejewski
, “
AFAR measurements of intensity and intensity moments
,”
J. Acoust. Soc. Am.
82
,
973
–
980
(
1987
).
Google Scholar
Crossref
Search ADS
 
5.
C.
Garrett
and
W. H.
Munk
, “
Space-time scales of internal waves
,”
Geophys. Fluid Dyn.
3
,
225
–
264
(
1972
).
Google Scholar
Crossref
Search ADS
 
6.
C.
Garrett
and
W. H.
Munk
, “
Space-time scales of internal waves: A progress report
,”
J. Geophys. Res.
80
,
291
–
297
(
1975
).
Google Scholar
Crossref
Search ADS
 
7.
W.
Munk
and
C.
Garrett
, “
Internal waves in the ocean
,”
Annu. Rev. Fluid Mech.
11
,
339
–
369
(
1979
).
Google Scholar
 
8.
R.
Esswein
and
S.
Flatté
, “
Calculation of the phase-structure function density from oceanic internal waves
,”
J. Acoust. Soc. Am.
70
,
1387
–
1396
(
1981
).
Google Scholar
Crossref
Search ADS
 
9.
S. M.
Flatté
and
R. B.
Stoughton
, “
Theory of acoustic measurement of internal wave strength as a function of depth, horizontal position, and time
,”
J. Geophys. Res.
91
,
7709
–
7720
(
1986
).
Google Scholar
Crossref
Search ADS
 
10.
J. S. Gerber, “Calculation by perturbative methods of the time coherence function of acoustic intensity from the effects of internal waves,” Ph.D. thesis, University of California at Santa Cruz, 1999.
11.
S.
Flatté
and
G.
Rovner
, “
Calculations of internal-wave-induced fluctuations in ocean-acoustic propagation
,”
J. Acoust. Soc. Am.
108
,
526
–
534
(
2000
).
Google Scholar
Crossref
Search ADS
PubMed
 
12.
R. Feynman and A. Hibbs, Quantum Mechanics and Path Ingetrals (McGraw-Hill, New York, 1965).
13.
R.
Dashen
and
G.-Y.
Wang
, “
Intensity fluctuation for waves behind a phase screen: A new asymptotic scheme
,”
J. Opt. Soc. Am. A
10
,
1219
–
1225
(
1993
).
Google Scholar
Crossref
Search ADS
 
14.
R. H.
Hardin
and
F.
Tappert
, “
Application of the split-step Fourier method to the numerical solution of nonlinear and variable coefficient wave equations
,”
SIAM Rev.
15
,
423
(
1973
).
Google Scholar
 
15.
S.
Flatté
and
F.
Tappert
, “
Calculation of the effect of internal waves on oceanic sound transmission
,”
J. Acoust. Soc. Am.
58
,
1151
–
1159
(
1975
).
Google Scholar
Crossref
Search ADS
 
16.
F. Jensen, W. Kuperman, M. Porter, and H. Schmidt, Computational Ocean Acoustics (AIP, New York, 2000).
17.
J.
Martin
and
S.
Flatté
, “
Intensity images and statistics from numerical simulation of wave propagation in 3-D random media
,”
Appl. Opt.
27
,
2111
–
2126
(
1988
).
Google Scholar
Crossref
Search ADS
PubMed
 
18.
A. W. Ellinthorpe, “The Azores Range,” Technical Report No. 4551, NUSC, New London, CT, 1973.
19.
B. G. Buehler, “Volume propagation experiments at the Azores fixed acoustic range,” Technical Report No. 5785, NUSC, New London, CT, 1979.
20.
S.
Reynolds
,
S.
Flatté
,
R.
Dashen
,
B.
Buehler
, and
P.
Maciejewski
, “
AFAR measurements of acoustic mutual coherence functions of time and frequency
,”
J. Acoust. Soc. Am.
77
,
1723
–
1731
(
1985
).
Google Scholar
Crossref
Search ADS
 
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