An explicit approximation to the wavelength of nonlinear waves |
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| Institution: | 1. Department of Civil Engineering, National Chiao-Tung University, Shinchu, Taiwan;2. Department of Hydraulics and Ocean Engineering, National Cheng-Kung University, Tainan, Taiwan;1. School of Ocean Sciences, Bangor University, Menai Bridge, Isle of Anglesey, LL59 5AB, UK;2. Institute of Marine and Atmospheric Research, Utrecht University, Princetonplein 5, 3584, CC Utrecht, The Netherlands;3. Research Institute for Applied Mechanics, Kyushu University, Kasuga, Fukuoka, 816-8580, Japan;1. Department of Physical Geography, Faculty of Geosciences, Utrecht University, P.O. Box 80.115, 3508 TC Utrecht, The Netherlands;2. Deltares, Dept. of Applied Geology and Geophysics, P.O. Box 85.467, 3508 AL Utrecht, The Netherlands;3. TNO Geological Survey of The Netherlands, P.O. Box 80.015, 3508 TA Utrecht, The Netherlands;4. Deltares, Marine and Coastal Systems Unit, Dept. of Applied Morphodynamics, P.O. Box 177, 2600 MH Delft, The Netherlands;1. Department of Geology, Ghent University, Krijgslaan 281-S8, 9000, Ghent, Belgium;2. Flanders Heritage Agency, Havenlaan 88, Bus 5, 1000, Brussels, Belgium;3. Department of Archaeology, Ghent University, Sint-Pietersnieuwstraat 35, 9000, Ghent, Belgium;4. GATE Archaeology, Hurstweg 8, 9000, Ghent, Belgium;5. Royal Belgian Institute of Natural Sciences, Vautierstraat 29, 1000, Brussels, Belgium |
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| Abstract: | An explicit and concise approximation to the wavelength in which the effect of nonlinearity is involved and presented in terms of wave height, wave period, water depth and gravitational acceleration. The present approximation is in a rational form of which Fenton and Mckee's (1990, Coastal Engng 14, 499–513) approximation is reserved in the numerator and the wave steepness is involved in the denominator. The rational form of this approximation can be converted to an alternative form of a power-series polynomial which indicates that the wavelength increases with wave height and decreases with water depth. If the determined coefficients in the present approximation are fixed, the approximating formula can provide a good agreement with the wavelengths numerically obtained by Rienecker and Fenton's (1981, J. Fluid Mech. 104, 119–137) Fourier series method, but has large deviations when waves of small amplitude are in deep water or all waves are in shallow water. The present approximation with variable coefficients can provide excellent predictions of the wavelengths for both long and short waves even, for high waves. |
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