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

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．

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 obtain by the coefficients value defined. The new form Boussinesq equation applying water depths range has been improved to h/l=0.8 with phase velocities and group velocities errors of less than 2%. A finite difference method is used to solve the equations. The results demonstrate that the new form of the Boussinesq equations can reasonably simulate several nonlinear effects.