Locus Method and Mode Calculation for Fluid Vibration in a Double Pipe

Abstract

A new computational technique to find zeroes and poles of complex functions has been developed. The idea is based upon the Cauchy's theorem: when the complex variable z describes an entire contour of a specified domain, the resultant locus of a complex function F(z) helps reveal number of its zeroes and poles within the domain. The procedure of the `locus'method is demonstrated with use of a spherical Bessel function of the second kind as an example. The method is also applied with success to detecting mode eigenvalues for viscous harmonic waves in a double pipe. Similarly to the Scarton's results for a single pipe, two different families of eigenvalues are evidently observed.