The coherence length of a horizontal array is the maximum separation between two points where coherent processing gives useful gain when a distant source is at broadside. In shallow water, the coherence length is limited by the environmental variability caused by several relevant oceanographic processes. In the present study, a statistical model is developed that quantifies how one oceanographic process, linear internal waves, affects the coherence length. A key input to the ocean sub-model is the vertically integrated energy density of the internal wave field. The acoustic sub-model is based on the adiabatic normal mode approximation and so should be reasonable for frequencies under 1 kHz. Numerical calculations using environmental data from the Shallow Water 2006 Experiment (SW06) show how the coherence length of individual modes varies with consequent effects on array coherence. The coherence length is shown to be a strong function of where the source and array are positioned in the water column. For a bottom-mounted array above a moderately lossy seabed, the model predicts a coherence length that depends only weakly on range, an effect observed in field experiments.
References
1.
W. M.
Carey
, “The determination of signal coherence length based on signal coherence and gain measurements in deep and shallow water
,” J. Acoust. Soc. Am.
104
, 831
–837
(1998
).2.
J. F.
Lynch
, T. F.
Duda
, and J. A.
Colosi
, “Acoustical horizontal array coherence lengths and the ‘Carey Number
,’ ” Acoust. Today
10
, 10
–19
(2014
).3.
W. M.
Carey
, J. F.
Lynch
, W. L.
Siegmann
, I.
Rozenfeld
, and B. J.
Sperry
, “Sound transmission and spatial coherence in selected shallow-water areas: Measurements and theory
,” J. Comput. Acoust.
14
, 265
–298
(2006
).4.
B. G.
Katsnel'son
and S. A.
Pereselkov
, “Low-frequency horizontal acoustic refraction caused by internal wave solitons in a shallow sea
,” Acoust. Phys.
46
, 684
–691
(2000
).5.
R.
Oba
and S.
Finette
, “Acoustic propagation through anisotropic internal wave fields: Transmission loss, cross-range coherence, and horizontal refraction
,” J. Acoust. Soc. Am.
111
, 769
–784
(2002
).6.
M.
Badiey
, Y.
Mu
, J.
Lynch
, J.
Apel
, and S.
Wolf
, “Temporal and azimuthal dependence of sound propagation in shallow water with internal waves
,” IEEE J. Ocean. Eng.
27
, 117
–129
(2002
).7.
T. F.
Duda
, J. M.
Collis
, Y-T.
Lin
, A. E.
Newhall
, J. F.
Lynch
, and H. A.
DeFerrari
, “Horizontal coherence of low-frequency fixed-path sound in a continental shelf region with internal-wave activity
,” J. Acoust. Soc. Am.
131
, 1782
–1797
(2012
).8.
H.
Cox
, “Spatial coherence?
,” J. Acoust. Soc. Am.
124
, 2522
(2008
).9.
S. M.
Flatté
, R.
Dashen
, W. H.
Munk
, K. M.
Watson
, and F.
Zachariasen
, “Linear internal waves
,” in Sound Transmission Through a Fluctuating Ocean
(Cambridge University Press
, New York
, 1979
), pp. 44
–62
.10.
D.
Rouseff
, “Effect of shallow water internal waves on ocean acoustic striation patterns
,” Waves Random Media
11
, 377
–393
(2001
).11.
M.
Abromowitz
and I. A.
Stegun
, Handbook of Mathematical Functions
(National Bureau of Standards
, Washington DC
, 1964
), Eq. 23.1.18.12.
S. A.
Reynolds
and M. D.
Levine
, DRI Internal Wave Simulations
, Tech. Memorandum APL-UW TM 5–04 (Applied Physics Laboratory
, Seattle
, 2005
).13.
F. S.
Henyey
, D.
Rouseff
, J. M.
Grochocinski
, S. A.
Reynolds
, K. L.
Williams
, and T. E.
Ewart
, “Effect of internal waves and turbulence on a horizontal aperture sonar
,” IEEE J. Ocean. Eng.
22
, 270
–280
(1997
).14.
M. D.
Levine
, “A modification of the Garrett-Munk internal wave spectrum
,” J. Phys. Ocean.
32
, 3166
–3182
(2002
).15.
W. A.
Kuperman
and D. R.
Jackson
, “Ocean acoustics, matched-field processing and phase conjugation
,” Imag. Complex Media Acoust. Seismic Waves Top. Appl. Phys.
84
, 43
–96
(2002
).16.
W. H.
Munk
, “A survey of internal waves and small-scale processes
,” in Evolution of Physical Oceanography
, edited by B. A.
Warren
and C.
Wunch
(MIT
, Cambridge, MA
, 1981
).17.
T. C.
Yang
and K.
Yoo
, “Internal wave spectrum in shallow water: Measurement and comparison with the Garrett–Munk model
,” IEEE J. Ocean. Eng.
24
, 333
–345
(1999
).18.
J.
Yang
, S.
Zhou
, J. X.
Zhou
, and J. F.
Lynch
, “Internal wave characteristics at the ASIAEX site in the east China Sea
,” IEEE J. Ocean. Eng.
29
, 1054
–1060
(2004
).19.
D.
Rouseff
and D.
Tang
, “Internal wave effects on the ambient noise notch in the East China Sea: Model/data comparison
,” J. Acoust. Soc. Am.
120
, 1284
–1294
(2006
).20.
S.
Kim
, W. A.
Kuperman
, W. S.
Hodgkiss
, H. C.
Song
, G. F.
Edelmann
, and T.
Akal
, “Robust time reversal focusing in the ocean
,” J. Acoust. Soc. Am.
114
, 145
–157
(2003
).21.
K. L.
Williams
, F. S.
Henyey
, D.
Rouseff
, S. A.
Reynolds
, and T. E.
Ewart
, “Internal wave effects on high-frequency acoustic propagation to horizontal arrays—experiments and implications to imaging
,” IEEE J. Ocean. Eng.
26
, 102
–112
(2001
).22.
B. G.
Katsnelson
, V. G.
Petnikov
, and J. F.
Lynch
, Fundamentals of Shallow Water Acoustics
(Springer
, New York
, 2012
), p. 124
.23.
M.
Badiey
, B. G.
Katsnelson
, J. F.
Lynch
, and S.
Pereselkov
, “Frequency dependence and intensity fluctuations due to shallow water internal waves
,” J. Acoust. Soc. Am.
122
, 747
–760
(2007
).24.
F. B.
Jensen
, W. A.
, Kuperman
, M. B.
Porter
, and H.
Schmidt
, “Normal modes
,” in Computational Ocean Acoustics
, 2nd ed. (Springer
, New York
, 2011
), pp. 337
–455
.25.
S. D.
Rajan
, J. F.
Lynch
, and G. V.
Frisk
, “Perturbative inversion methods for obtaining bottom geoacoustic parameters in shallow water
,” J. Acoust. Soc. Am.
82
, 998
–1017
(1987
).26.
D. E.
Weston
and K. J.
Stevens
, “Interference of wide-band sound in shallow water
,” J. Sound Vib.
21
, 57
–64
(1972
).27.
V.
Petukhov
, “Fundamental directions of investigations of interference phenomena observed in the propagation of broadband acoustic signals in oceanic waveguides (review of publications by Russian scientists)
,” in Ocean Acoustic Interference Phenomena and Signal Processing
, edited by W. A.
Kuperman
and G. L.
D'Spain
(AIP
, New York
, 2002
), pp. 3
–10
.28.
29.
A.
Ishimaru
, Wave Propagation and Scattering in Random Media
(Academic
, New York
, 1978
), p. 356
.30.
E. P.
Gulin
and Yu. P.
Lysanov
, “Soviet and Russian studies of underwater sound scattering and acoustic signal fluctuations
,” in History of Russian Underwater Acoustics
, edited by O. A.
Godin
and D. R.
Palmer
(World Scientific Publishing
, Hackensack, NJ
, 2008
), pp. 121
–196
.31.
F. S.
Henyey
, “Sound through internal waves: Difficult cases
,” in Proceedings of ‘Aha Huliko’a Hawaiian Winter Workshop
(1997
), pp. 175
–180
.32.
A. A.
Lunkov
and V. G.
Petnikov
, “The coherence of low-frequency sound in shallow water in the presence of internal waves
,” Acoust. Phys.
60
, 61
–71
(2014
).33.
D. B.
Creamer
, “Scintillating shallow-water waveguides
,” J. Acoust. Soc Am.
99
, 2825
–2838
(1996
).34.
K. B.
Winters
and E. A.
D'Asaro
, “Direct simulation of internal wave energy transfer
,” J. Phys. Oceanogr.
27
, 1937
–1945
(1997
).35.
F. S.
Henyey
and S. A.
Reynolds
, “A numerical simulator of ocean internal waves for long-range acoustics
,” Technical Memorandum APL-UW TM 1–13 (March 2013
).36.
D. J.
Tang
, J. N.
Moum
, J. F.
Lynch
, P.
Abbot
, R.
Chapman
, P. H.
Dahl
, T. F.
Duda
, G.
Gawarkiewicz
, S.
Glenn
, J. A.
Goff
, H.
Graber
, J.
Kemp
, A.
Maffei
, J. D.
Nash
, and A.
Newhall
, “Shallow Water'06: A Joint Acoustic Propagation/Nonlinear Internal Wave Physics Experiment
,” Oceanography
20
,156
–167
(2007
).37.
A. E.
Newhall
, T. F.
Duda
, K.
von der Heydt
, J. D.
Irish
, J. N.
Kemp
, S. A.
Lerner
, Y-T.
Lin
, J. F.
Lynch
, A. R.
Maffei
, A. K.
Morozov
, A. A.
Shmelev
, C. J.
Sellers
, and W. E.
Witzell
, “Acoustic and oceanographic observations and configuration information for the WHOI moorings from the SW06 experiment
,” Technical Report WHOI-2007–04
(URI: http://hdl.handle.net/1912/1826) (May 2007
).38.
V. M.
Kuz'kin
, Y-T.
Lin
, A. A.
Lunkov
, J. F.
Lynch
, and V. G.
Petnikov
, “Frequency shifts of the sound field interference pattern on oceanic shelf in summer conditions
,” Acoust. Phys.
57
, 381
–390
(2011
).39.
M. H.
Orr
, B. H.
Pasewark
, S. N.
Wolf
, J. F.
Lynch
, T.
Schroeder
, and C-S.
Chiu
, “South China Sea internal tide/internal waves—impact on the temporal variability of horizontal array gain at 276 Hz
,” IEEE J. Ocean. Eng.
29
, 1292
–1307
(2004
).40.
R. H.
Headrick
, J. F.
Lynch
, J. N.
Kemp
, A. E.
Newhall
, K.
von der Heydt
, J.
Apel
, M.
Badiey
, C-S.
Chiu
, S.
Finette
, M.
Orr
, B.
Pasewark
, A.
Turgot
, S.
Wolf
, and D.
Tielbuerger
, “Modeling mode arrivals in the 1995 SWARM experiment acoustic transmissions
,” J. Acoust. Soc. Am.
107
, 221
–236
(2000
).© 2015 Acoustical Society of America.
2015
Acoustical Society of America
You do not currently have access to this content.