Improved explicit approximation of linear dispersion relationship for gravity waves: A discussion |
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| Institution: | 1. Department of Marine Technology, Amirkabir University of Technology, Hafez Ave. No. 424, Tehran, Iran;2. Department of Civil Engineering, Pardis Branch, Islamic Azad University, Tehran, Iran;1. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116023, China;2. Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs. Lyngby, Denmark |
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| Abstract: | Recently, an accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship (Beji, 2013). The author has nicely improved Eckart's explicit dispersion relationship by introducing an empirical correction function. The resulting expression is valid for the entire range of relative water depths and accurate to within 0.044%.In this discussion, the proposed expression by the author is simplified and improved to an accuracy of 0.019%. Moreover, a near exact solution with 0.001% accuracy is also given. |
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