An Asymptotic Formula for the Prolate Spheroidal Radial Function of the Third Kind.
Abstract
In carrying out a program to investigate the interaction of discrete noise sources (such as patches of cavitation) with submerged vehicle hulls, an asymptotic high-frequency analysis involving prolate spheroidal bodies has been used. The problem is approximated as that of a monopole sound source arbitrarily located with respect to a pressure release (soft) prolate spheroid of arbitrary fineness ratio. The solution is an infinite sum of spheroidal harmonics, where it has been shown that the sum can be terminated before approximately kL/2 terms (k=wave number, L=length of body) when the sound source is many wavelengths away from the body. When the source is near the body, however, slightly more than kL/2 terms are required for convergence. It is for this range that a new asymptotic formula for the spheroidal radial function was required, i.e. one valid for kL/2 large and the order greater than kL/2. This memorandum describes an integral representation of this function valid for the desired range of independent variables. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 21, 1976
- Accession Number
- ADA024352
Entities
People
- G. C. Lauchle
Organizations
- Pennsylvania State University