A Numerical Technique for the Calculation of Dispersion Relations and Mode Functions for Upper Ocean Internal Waves

摘要

This paper is concerned with calculating the internal wave eigenfunctions and dispersion relations for an infinitely deep ocean with an arbitrary Vaisala frequency profile. The method involves numerically integrating the differential equation from a depth where the profile is essentially an exponential function, and therefore where the eigenfunctions are known explicitly, to the surface where each eigenfunction must vanish. The equation that is implied by the surface boundary condition determines the dispersion relation, which is obtained numerically by solving the equation by means of the method of regula falsi. A computer program that performs the necessary calculations is described and listed.