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Energy Properties for Higher-Order Stokes Waves over Horizontal Bottom

Author(s): Xiang Gao; Xiaozhou Ma; Yuxiang Ma; Guohai Dong; Junliang Gao

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Keywords: Energy; Nonlinear wave; Analytical solution

Abstract: The energy in the surface water waves is a very important concept. The most common method for calculating the wave energy is based on the linear or the first-order Stokes wave theory, where the phaseaveraged potential, kinetic and total energy of waves is a function of just the amplitude or the height of the waves and the kinetic energy is equal to the potential energy. Because of its simplicity, this method is used for nonlinear waves as well. In this paper, the phase-averaged energy properties, i.e., potential, kinetic and total energy of very nonlinear waves in finite water depth and deep water over horizontal bottoms are studied. The analytical expressions of the wave energy properties are derived based on the nonlinear wave theories, such as the second-, third- and fifth-order Stokes wave theories. The energy are accurate to fourth order, sixth order and tenth order respectively. The results show that, for the nonlinear wave, the energy is no longer a singlevariable function of wave height and varies with the wave parameters such as wave height and wave number. Besides, the kinetic energy and potential energy are not equal, the kinetic energy is larger than potential energy. Comparison between the energy of Airy waves and that of nonlinear waves has shown that cautions should be taken to calculate the energy of waves of high nonlinearity.

DOI:

Year: 2020

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