TRUNCATION ORDER OF FOURIER WAVE THEORY

Rodney J. Sobey

Abstract


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.

Keywords


Fourier Theory; truncation; truncation order

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