Improved explicit approximation of linear dispersion relationship for gravity waves: Comment on another discussion |
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| Institution: | 1. Sustainable Arctic Marine and Coastal Technology (SAMCoT), Centre for Research-based Innovation (CRI), Norwegian University of Science and Technology (NTNU), Trondheim, Norway;2. The University Centre in Svalbard (UNIS), Longyearbyen, Spitsbergen, Norway;3. Faculty of Civil Engineering and Geosciences, Delft University of Technology, Delft, The Netherlands;4. Department of Structural Engineering, Norwegian University of Science and Technology, Trondheim, Norway |
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| Abstract: | Recently, a simple explicit approximation to linear dispersion relationship with an accuracy of 0.044% has been proposed (Beji, 2013). Then, this solution was simplified and improved to an accuracy of 0.019% (Vatankhah and Aghashariatmadari, 2013). Moreover, by considering Beji's approximation as a seed, Newton's method was used (Simarro and Orfila, 2013) to obtain an accurate and explicit two-step solution to linear dispersion relationship with percentage error less than 0.0000082%.Newton's method works very well, if a good seed is given. In this discussion, Beji's expression is simplified and improved as a seed for Newton's method. Using this new expression (initial guess), the solution is improved to an accuracy of 0.00000028% which is 30 times smaller than the solution proposed by Simarro and Orfila (2013). |
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