The Application of Canonical Eigenvalues to Two-Layer, Bounded, Underwater Acoustic Ducts
Abstract
This report applies the method of canonical eigenvalues to double- duct propagation of underwater acoustics. The class of two-layer bounded profiles with free- or rigid-boundary conditions is treated. The canonical eigenvalue equation contains two parameters. (The conventional approach has six parameters). Eigenvalue solutions are presented for 23 sets of parameters and boundary conditions. These solutions can be applied to any equivalent wave problem in any discipline of physics. Physical results are presented for six sound-speed profiles. These include plots versus frequency of phase velocity, group velocity, and eigenfunction normalization coefficients. Eleven examples of eigenfunctions (standing waves) are presented. At the critical frequencies of maximum coupling between ducts, the phase velocities of adjacent modes are pinched toward each other, the group velocity and eigenvalue normalization curves for adjacent modes cross each other, and the eigenfunction amplitudes of adjacent modes strongly resemble each other. The report develops an unexpected example in which two radically different profiles have identical plots of phase and group velocity as a function of frequency. Special configurations, predicted by ray theory as degenerate, do not lead to degenerate eigenvalues. The theory is extended to treat sound-speed discontinuities and layers of different constant density.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1991
- Accession Number
- ADA239641
Entities
People
- D. Gordon
- F. Hosmer
- M. A. Pedersen