Improved explicit approximation of linear dispersion relationship for gravity waves |
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| Affiliation: | 1. Department of Mechanical and Manufacturing, Mondragon University, Loramendi 4 Apdo. 23, 20500, Arrasate, Spain;2. Department of NE and Fluid Mechanics, University of the Basque Country (UPV/EHU), Otaola 29, 20600, Eibar, Spain;3. Department of Applied Physics II, University of the Basque Country (UPV/EHU), B. Sarriena s/n, 48940, Leioa, Spain;4. Joint Research Unit (UPV/EHU-IEO) Plentziako Itsas Estazioa, University of Basque Country (UPV/EHU), Areatza Hiribidea 47, 48620, Plentzia, Spain;5. Centre for Ocean Energy Research, Maynooth University, Maynooth, Co., Kildare, Ireland;1. College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao, 266590, China;2. School of Division of Mathematics and Artificial Intelligence, Qilu University of Technology, Jinan, 250200, China;1. College of Engineering, Ocean University of China, Qingdao 266100, China;2. Shandong Province Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao 266100, China;3. Science and Technology on Underwater Vehicle Laboratory, Harbin Engineering University, Harbin, 150001, China;1. Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97835, Mexico;2. Department of Civil Engineering, Queen''s University, Kingston, ON, K7L 3N6, Canada |
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| Abstract: | For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given. |
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