lect_121 - COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12...

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Unformatted text preview: COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12 Computational Ocean Acoustics • Ray Tracing • Wavenumber Integration • Normal Modes • Parabolic Equation COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12 Normal Modes • Mathematical Derivation – Point and Line Sources in Waveguide (5.2) • Modal Expansion of Depth-Dependent Green’s Function (5.3) • Ideal Waveguide (5.4) – Generalized Derivation (5.5) • Pekeris Waveguide • Virtual Modes – Deep Water Problem – The Munk Profile (5.6) • Numerical Approaches – Finite Difference Methods (5.7.1) – Layer Methods (5.7.2) – Shooting Methods (5.7.3) – Root Finders (5.7.4) COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12 1 2 3 C Re(k r ) Im(k r ) Complex k r-plane C EJP C ∞ C ∞ + ω /c- ω /c Location of eigenvalues for the Pekeris problem using the EJP branch cut. COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12 Branch Cut Selection EJP Branch Cut Complex Square Root Z = R exp ( i θ ) = R exp ( i θ+ n 2π) Z = R...
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This note was uploaded on 02/24/2012 for the course MECHANICAL 2.068 taught by Professor Henrikschmidt during the Spring '03 term at MIT.

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lect_121 - COMPUTATIONAL OCEAN ACOUSTICS 13.853 Lecture 12...

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