Analysis of Natural Waves by Local Approximations

Abstract

Local approximations are recommended as a tool for the analysis of natural water waves. The particular class of local approximations described is based on local fitting of a sine curve, which leads naturally to the definition of locally defined frequencies. As a specific application, two methods are outlined for estimating surface elevations of large (nonlinear) waves from subsurface pressures. One of the methods is simple enough to be condensed into a single formula that expresses the surface elevation in terms of three pressure readings. Yet, its accuracy is better than that of the traditional spectral transfer method. Guidelines are presented for the use of the methods in connection with real (noisy) data.