A Simple Scheme for High-Order Nonlinear Normal Mode Initialization

Abstract

An algorithm for obtaining high-order mode initialization of the type first proposed by Baer and Tribbia is developed which is free from the major difficulty of previous methods?the necessity of calculating Frechet derivatives of the nonlinear terms. This new method is shown to be a logical extension of the technique proposed by Machenhauer; thus the asymptotic equivalence of the Machenhauer and Baer-Tribbia initialization methods is accomplished. A comparison between the new algorithm and the older method of calculating second-order initialization demonstrates the accuracy and ease of implementation of the new technique.