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The dispersion relations of a wave in current
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DOI：10.1016/j.apor.2026.105077.png)
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Abstract
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• It is found that the roots of the dispersion equation for the evanescent modes derived in the space-fixed coordinate system are complex. • The existing ranges of the complex roots are analyzed, and reasonable initial values are given for computation of the complex roots by an iterative method. • First order approximation of the wave dispersion relation to the dimensionless current parameter is examined by comparing with the exact solution of the wave dispersion relation. The limitation condition of the first order approximation is proposed.
Keywords:
Wave and current
Dispersion relation
Eigenfunction expansion
First order approximation
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