Evaluation of the Wavelike Disturbance in the Kelvin Wave Source Potential

Abstract

This paper discusses the numerical evaluation of the characteristic Kelvin wavelike disturbance trailing downstream from a translating submerged source. Mathematically the function describing the wavelike disturbance is expressed as a single integral with infinite integration limits and a rapidly oscillatory integrand. Numerical integration of such integrals is both cumbersome and time-consuming. Attention is therefore focused on two complementary Neumann-series expansions which were originally derived by Bessho [1].2 Numerically stable algorithms are presented for the accurate and efficient evaluation of the two series representations. When used in combination with the Chebyshev expansions for the nonoscillatory near-field component which were recently obtained by Newman [2], the present algorithms provide an effective solution to the numerical difficulties associated with the evaluation of the Kelvin wave source potential.