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本文在Bousinesq的浅水波假定下,采用各层内任意点ziα速度水平分量代替传统的垂向平均速度,推导出了各层速度的三个分量及压力由各层内点ziα速度水平分量表示的沿垂向分布,将三维问题简化为二维问题,建立了二层流体浅水波演化模型,即二层流体的改进Bousinesq方程组.在该方程组中,随ziα距交界面距离不同,该二层流体浅水波演化模型具有不同的色散特性和非线性.作者证明文中参数αi皆取-0393时,该方程组具有最佳的色散特性.该方程组不仅适于模拟波浪沿水平方向从深水域向浅水域传播时的折射、绕射和反射问题,而且也适用于研究在浅水或中等水深的水域中波浪传播问题
Based on the shallow water wave assumption of Bousinesq, the horizontal component of ziα velocity at arbitrary point in each layer is used instead of the traditional vertical average velocity, and the three components of each layer velocity and the pressure are expressed by the horizontal component of ziα velocity in each layer Along the vertical distribution, the three-dimensional problem is reduced to a two-dimensional problem, and a two-layer fluid shallow water evolution model is established, which is an improved Bousinesq equation for two-layer fluid. In this system, the shallow water wave evolution model of the two-layer fluid has different dispersion characteristics and nonlinearities as the distance between zaα and the interface is different. The author proves that when the parameters αi are -0393, the system has the best dispersion property. The equations are not only suitable for simulating the refraction, diffraction and reflection problems of wave propagation in the horizontal direction from deep to shallow waters, but also for studying wave propagation in shallow or medium water depths