Spectrum Evolution of Three-Dimensional Focused Wave Groups Based on Modified Nonlinear Schr?dinger Equation
The modified fourth-order nonlinear Schrödinger equation(MNLSE),the third-order nonlinear Schrödinger equation of(NLSE)and the linear equation,are numerically solved to generate directionally evolving three-dimensional focusing waves in deep water,and the spectral characteristics of the generated waves as well as the characteristics of the evolution process,including a comparative study is made on the spectral characteristics of the generated waves and their evolution in terms of energy transfer,change in wave steepness,change in average wave number and change in bandwidth.It is found that there is energy transfer to high and low wave numbers during the evolution of the two nonlinear evolution models,which leads to changes in the wave shape,and the nonlinearity also affects the changes in the parameters of the focusing wave steepness,the time required for the wave to reach the focus,and the change in the bandwidth,etc.Moreover,the above features are significantly different between the two nonlinear models,and the results show that the wave features of the fourth-order MNLS evolution are superior to those of the third-order MNLS evolution.
nonlinear Schrödinger equation(NLSE)three dimensional focused wave groupspectral evolutionenergy transfer
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