Ocean Acoustic Theory
• Acoustic Wave Equation
• Integral Transforms
• Helmholtz Equation
• Source in Unbounded and Bounded Media
• Propagation in Layered Media
– Reflection and Transmission
• The Ideal Waveguide
– Image Method
– Wavenumber Integral
– Normal Modes
• Pekeris Waveguide
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COMPUTATIONAL OCEAN ACOUSTICS
Horizontally stratified environment
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Superposition Principle
Source contribution:
Homogeneous Solution:
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Mag
nit
ud
e
50 F = 150 Hz
40
30
20
Evanescent Radiating Waves
Waves 10
0 0.2 0.4 0.6 0.8 1.0
Horizontal wavenumber (m-1)
Magnitude of the depth-dependent Green’s function for point source in an
infinite medium. Solid curve: z – z = Ȝ/10; dashed curve: z – zs = 2 Ȝ.s
4 COMPUTATIONAL OCEAN ACOUSTICS Lecture 5
Example: Hard Bottom – c2 > c1
Medium 1 Radiating Evanescent
0 k2 k1
Medium 2 Radiating Evanescent
| R | < 1 | R | = 1 | R | < 1
[See Fig 2.10 in Jensen, Kuperman, Porter and Schmidt. Computational Ocean Acoustics.
New York: Springer-Verlag, 2000.]
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Idealized ocean waveguide model with pressure-release surface and bottom
Ideal Fluid Waveguide Image Method
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1234
5
6
7
C
Re(kr)
r)
r
+ Ȧ/c- Ȧ/c
Im(k
Complex k -plane
Singularities of the depth-dependent Green’s function for an ideal waveguide.
8 COMPUTATIONAL OCEAN ACOUSTICS Lecture 5 13.853
Im(kr)
7 Mode Mode Mode
1 2 3 -0 -0 -06 Complex kr-plane
5
4 3 2 1 Re(kr) 50 50 50
C
100 100 100 -1 0 1 -1 0 1 -1 0 1
- Ȧ/c + Ȧ/c Depth dependence of the first 3 normal modes in
Singularities of the depth-dependent Green’s function for an ideal waveguide. ideal waveguide at 20Hz.
Dep
th (
m)
9 COMPUTATIONAL OCEAN ACOUSTICS Lecture 5 13.853
[see Jensen, Fig 2.21] [see Jensen, Fig 2.22]
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[see Jensen, Figs 2.23 & 2.24]
Lecture 5
COMPUTATIONAL OCEAN ACOUSTICS
Pekeris waveguide with pressure-release surface and penetrable fluid bottom
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Mode Mode Mode1 2 3
-0 -0-0
50 5050
Dep
th (
m)
100 100100
150 150150 -1 0 1 -1 0 1 -1 0 1
Depth dependence of acoustic pressure for the 3 normal modes in the Pekeris waveguide at 35Hz.
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[see Jensen, Fig 2.28]
Lecture 5
COMPUTATIONAL OCEAN ACOUSTICS
[see Jensen, Fig 2.29]
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[see Jensen, Fig 2.30]
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