An Asymptotic Formula for the Prolate Spheroidal Radial Function of the Third Kind.
PENNSYLVANIA STATE UNIV UNIVERSITY PARK APPLIED RESEARCH LAB
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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 kL2 terms kwave number, Llength of body when the sound source is many wavelengths away from the body. When the source is near the body, however, slightly more than kL2 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 kL2 large and the order greater than kL2. This memorandum describes an integral representation of this function valid for the desired range of independent variables. Author
- Marine Engineering