Accuracy Examination of the Fourier Series Approximation for Almost Limiting Gravity Waves on Deep Water

A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, wh...

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Bibliographic Details
Published in:Mathematical and computational applications 2024-01, Vol.29 (1), p.5
Main Authors: Chen, Yang-Yih, Chang, Hsien-Kuo
Format: Article
Language:English
Subjects:
Accuracy
Analysis
angled crest
Approximation
Boundary conditions
collocation method
Constraining
Deep water
Experiments
Fourier series
Free surfaces
Gravity waves
inner profile
Kinematics
Mathematical analysis
Methods
Numerical analysis
Physical properties
radius of curvature
Water waves
Wave crest
Wave propagation
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Summary:A permanent gravity wave propagating on deep water is a classic mathematical problem. However, the Fourier series approximation (FSA) based on the physical plane was examined to be valid for almost waves at all depths. The accuracy of the FSA for almost-limiting gravity waves remains unevaluated, which is the purpose of this study. We calculate some physical properties of almost-limiting waves on deep water using the FSA and compare them with other studies on the complex plane. The comparison results show that the closer the wave is, the greater the difference. We find that the main reason for this difference is that the wave profile in the FSA retains an original implicit form and is not represented by Fourier series. Therefore, the kinematic and dynamic conditions of the free surface around the wave crest cannot be satisfied at the same time.
ISSN:2297-8747
1300-686X
2297-8747
DOI:10.3390/mca29010005