Open AccessTRUNCATION ORDER OF FOURIER WAVE THEORY
Author(s) -
Rodney J. Sobey
Publication year - 1988
Publication title -
proceedings of conference on coastal engineering/proceedings of ... conference on coastal engineering
Language(s) - English
Resource type - Journals
eISSN - 2156-1028
pISSN - 0589-087X
DOI - 10.9753/icce.v21.21
Subject(s) - truncation (statistics) , truncation error , fourier series , fourier transform , mathematics , mathematical analysis , boundary (topology) , crest , range (aeronautics) , physics , statistics , optics , materials science , composite material
Specific consideration is given to the dependence of Fourier wave solutions on both truncation order and the number of free surface nodes. Solution dependence is quantified by a comprehensive set of numerical experiments over a typical range of wave height, water depth, truncation order and overspecification values. Integral error measures include the rms free surface boundary condition errors and a slope error that identifies non-physical positive slope segments in the wave profile between crest and trough. Summary error diagrams are presented as a guide to the adoption of suitable truncation orders and overspecification for Fourier solutions. The truncation order is the crucial parameter but there is measurable advantage is some small overspecification.