Computational Ocean Acoustics - MIT OpenCourseWare...13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 6...
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COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 6 Computational Ocean Acoustics • Ray Tracing • Wavenumber Integration • Normal Modes • Parabolic Equation
Transcript of Computational Ocean Acoustics - MIT OpenCourseWare...13.853 COMPUTATIONAL OCEAN ACOUSTICS Lecture 6...
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
Computational Ocean Acoustics
• Ray Tracing• Wavenumber Integration• Normal Modes• Parabolic Equation
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
Wavenumber Integration• Range-independent – Integral Transform solution• Exact depth-dependent solution• Numerical issues:
– Numerical stability of depth solution– Evaluation of inverse transforms
• Example: Pekeris waveguide– Relation to Normal Mode solution
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
Horiztonally stratified environment
z
layer 1: upper halfspacer
. . .
. . .
layer 2
layer mlayer m + 1
layer N: lower halfspace
Interface 1Interface 2
Interface m
Interface N - 1
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 62 Unknowns
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
Point source in n2-linear fluid medium
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
2 Unknowns
See Fig 10.6 and 10.7, “Bessel Functions of Fractional Order,”in Abramowitz, M. and Stegun, I. Handbook of Mathematical Functions.
Mineola NY: Dover, 1965
See Fig 10.6 and 10.7, “Bessel Functions of Fractional Order,”in Abramowitz, M. and Stegun, I. Handbook of Mathematical Functions.
Mineola NY: Dover, 1965
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
4 Unknowns
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
1
2
3
2
4
Number ofBoundaryConditions
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COMPUTATIONAL OCEAN ACOUSTICS13.853 Lecture 6
Elastic Ice Cover
Fluid Water Column
Fluid Sediment Layer
Elastic Sediment Layer
Elastic Halfspace
BoundaryConditions
WavefieldUnknowns
Vacuum0
4
2
2
4
2
23
2
3
4
14 unknowns 14 equations
Global Equations and Unknowns
Computational Ocean AcousticsWavenumber Integration
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