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促进其线性频散特征另一种形式的Bousinesq方程

ALTERNATIVE FORM OF THE BOUSSINESQ EQUATIONS WITH IMPROVED LINEAR DISPERSION CHARACTERISTICS

  • 摘要: Bousinesq方程能够用于模拟表面重力波传播过程中的折射、绕射、反射以及浅化,非线性作用等现象.用不同垂直积分方法所得到的二维Boussinesq方程形式具有不同的线性频散特征.采用两个不同的水深层的水平速度变量组合,推导出一个新形式的Bousinesq方程.通过对其参数的设置可得到精确的线性频散解Pade近似4阶精度.其适用范围已由原来的浅水,向深水拓进.相速误差小于2%,其拓展适用范围可达到08个波长水深.应用所得到的新型Bousinesq方程,采用有限差分法,对经典工况进行了数值模拟,其计算结果表明,计算值与物模实验值吻合较好.这说明本文新形式的Boussinesq方程对变水深非线性效应所产生的能量频散有着较为精确的描述

     

    Abstract: Boussinesq type equations, can be used to simulate the nonlinear transformation of surface waves due to the effects of shoaling, refraction, diffraction, reflection and nonlinear action so on. Different linear dispersion charateristics can be obtained by different vertically integrated methods. A new form of the Boussinesq equations is derived by using two different layers the horizontal velocity variable. The 4th order of Pade approximation, that is exact linear dispersion relation of Airy waves, is obta...

     

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