Factorization of the Characteristic Equation for Three Layer Ducts
Abstract
The characteristic equation for a lossy three-layer ocean model is complex and transcendental and thus requires numerous, lengthy iterations to determine its eigenvalues. Factoring the equation, made possible by the introduction of a small error term, provides new equations that are quickly and easily solved. The eigenvalues of the simplified equations are examined and compared with those of the original characteristic equation for two water/ sediment/bedrock models. The first model treats all three layers as liquids which can propagate only compressional waves. The second model represents both the sediment and bedrock layers as elastic materials with support the propagation of shear waves in addition to compressional waves. For the all- liquid model, the factored solutions showed too much mode attenuation compared to the exact solutions. A different type of factor was developed that had eigenvalues closer to the exact eigenvalues. The liquid/elastic/elastic model factored solutions also predicted solutions also predicted too much loss, but no correction was found. Keywords: Mathematical models; Equations; Ducts; Ocean waves.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jul 01, 1990
- Accession Number
- ADA223867
Entities
People
- D. F. Mccammon
- E. B. Brosius
Organizations
- Pennsylvania State University