一种高效改进双层Boussinesq型水波方程速度场的方法

AN EFFICIENT METHOD FOR IMPROVING THE VELOCITY FIELD OF THE TWO-LAYER BOUSSINESQ MODEL

  • 摘要: 为拓宽最高空间导数为2的双层Boussinesq型水波方程的速度适用范围,该文针对水体水平和垂向速度分别构造了一种包含5个参数的新函数,以刻画沿水深方向的速度特征。采用非线性最小二乘法对该方程速度场进行拟合,从而优化这些参数取值。为检验此方法的有效性,选取Stokes线性波、波浪流函数以及聚焦波的速度场展开对比分析。研究结果表明,该方法能有效降低方程速度场的误差,可将方程的速度适用范围拓宽约3倍。通过对整个波长的流函数和多个kh的线性波叠加后的速度场予以比较,进一步验证了该方法的适用性。

     

    Abstract: In order to extend the velocity application range of the two-layer Boussinesq model with the highest spatial derivative of 2, a new function with five parameters is constructed in this study for the horizontal and vertical velocities of the water body, to describe the velocity characteristics along the water depth direction. The nonlinear least square method is used to fit the velocity field of this model, so as to optimize the values of these parameters. To test the effectiveness of this method, the velocity fields of Stokes linear wave, of the stream-function, and of the focused wave are selected for comparison. The research results show that this method can effectively reduce the error in the velocity field of the equation and broaden the applicable velocity range by approximately three times. By comparing the stream function across the entire wavelength with the velocity field formed through superposition of multiple kh linear waves, the applicability of this approach has been further validated.

     

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