# Accession Number:

## ADA222812

# Title:

## Canonical Eigenvalues. Part 1. General Theory

# Descriptive Note:

## Technical rept. Mar 1986-Jul 1989,

# Corporate Author:

## NAVAL OCEAN SYSTEMS CENTER SAN DIEGO CA

# Personal Author(s):

# Report Date:

## 1990-02-01

# Pagination or Media Count:

## 21.0

# Abstract:

A formulation of the eigenvalue problem, here referred to as the canonical eigenvalue method or canonical eigenvalue theory, was developed to facilitate analysis of mode coupling effects in double ducts in underwater acoustics. This canonical eigenvalue method can also be used if eigenvalue curves as a function of some variable parameter, such as frequency, are required to analyze some acoustic phenomenon. Also, if one or more eigenvalues are required at many values of such a parameter, as for instance in broadband simulations, the canonical eigenvalue method is a useful eigenvalue computation technique. This report is one of a series of reports that explain the canonical eigenvalue method and demonstrate its application to various acoustic ducts, including some double ducts. The chief objective of this report is to present the general theory of canonical eigenvalues. In the approach taken here, the eigenvalue equation is couched in purely mathematical terms, involving two dimensionless variables and a set of dimensionless parameters related to the sound-speed profile. The physical quantities of interest, such as frequency and phase and group velocity, are generated after the eigenvalues have been determined. This approach has a number of advantages over customary approaches. kr

# Descriptors:

# Subject Categories:

- Theoretical Mathematics