Boussinesq方程的发展形式与Airy波理论差异性研究

A Study of Difference Between The Developing form of Boussinesq equation and Airy Wave

应用势流理论，采用递推函数方法推导出一个新形式的Ｂｏｕｓｉｎｅｓｑ方程。通过对新方程的参数设置，可以讨论出Ｂｏｕｓｓｉｎｅｓｑ方程发展趋势和不同的发展形式。对浅水波动的描述方程，Ｂｏｕｓｓｉｎｅｓｑ方程的发展趋势为适用水深范围的拓展。拓展应用范围的大小则由其方程频散特征向Ａｉｒｙ波频散解逼近程度来决定。而Ｂｏｕｓｉｎｅｑ方程又不同于Ａｉｒｙ波，主要原因是Ｂｏｕｓｓｉｎｅｓｑ方程中含有线性频散项，Ａｉｒｙ波则只是长波首项近似，无线性频散项。其频散特征为精确的线性频散解。对实际水波传播而言，Ａｉｒｙ波理论的局限性是不言而喻的。

In the paper, a new form of the Boussinesq equation is derived by the theory of potent function with method of recurrence formula. Developing tendency and different form of the Boussinesq equation may be discussed by setting up some parameters of the Boussinesq equation. For shallow water wave propagation, the developing tendency is to increase the range of the equation to fit water depth. The range increased is made by the degree approximative of dispersion characteristics of the Boussinesq equation to dispersion characteristic of Airy wave. The Boussinesq equation differs fram Airy wave is that Boussinesq equation includes the term of dispersion and Airy wave has not the dispersion charaterirtic term. Airy wave is approximate to only the largest term of long wave, although Airy wave has accurate solution of dispereion. So Airy wave has vary large limit in simulating water wave propagation.