EVALUATION OF THE WAVELIKE DISTURBANCE IN THE KELVIN WAVE SOURCE POTENTIAL

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. 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 that were recently obtained by Newman, the present algorithms provide an effective solution to the numerical difficulties associated with the evaluation of the Kelvin wave source potential.